21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read...
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Transcript of 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read...
![Page 1: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/1.jpg)
21(x * x *x) ÷ 7 (x*x)
Otcq
![Page 2: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/2.jpg)
Aim 2-1: How do we define and simplify rational expressions?
HWk read 2-1 p 67# 1-10
Objective: SWBAT Simplify a Rational Expression.
![Page 3: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/3.jpg)
Objectives:1.SWBAT to define a rational expression.2.SWBAT to simplify a rational expression to its simplest form.3. SWBAT to find prohibited values for variables in denominators that would make an expression undefined.4. SWBAT to +, -, * and ÷ with rational expressions and then to factor and to simplify rational expressions.
![Page 4: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/4.jpg)
Review: Laws of Exponents
amnMultiplying Powers: *
m na a
![Page 5: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/5.jpg)
Laws of Exponents
am n
amn
ambm
Dividing Powers:
Power of a Power:
Power of a Product:
m
n
a
a
nma
mab
![Page 6: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/6.jpg)
Laws of Exponents
1
an
an
Negative Exponents:
na
1n
a
![Page 7: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/7.jpg)
Laws of Exponents n
a
b
Power of a Quotient:
Power of Zero: 0a
n
n
a
b
1
nb
a
n
n
a
b
![Page 8: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/8.jpg)
Examples using the laws of exponents:
1. 2ab2 3a4b2c 6a5b4c
2. 6x2y3 xyz 6x3y4z
3. x12
x4 x8
![Page 9: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/9.jpg)
Definition: A Rational Expression is the quotient of two polynomials with the denominator not equal to zero.
25
2
m+4 8x 2 5, , , x
m-4 4x 5
x x
y x
![Page 10: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/10.jpg)
EXCLUDED VALUES IN DENOMINATORS
Any value of x that makes the denominator = 0 is prohibited from the expression.
Why?
Because an expression is undefined when its denominator is equal to 0.
![Page 11: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/11.jpg)
![Page 12: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/12.jpg)
For test show algebra: x+ 2 = 0 -2 -2 x = - 2
![Page 13: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/13.jpg)
If x= -1, then -1 + 1 = 0.
The expression is undefined when a variable value makes the denominator equal to 0
Answer: 7
x 1
![Page 14: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/14.jpg)
RECALL:
Rational number = any number that may be expressed as a quotient of two integers with no 0 denominator.
Now we have:
Rational expression = any expression that may be stated as a quotient of two polynomials with no 0 denominator.
![Page 15: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/15.jpg)
Remember, denominators cannot = 0.
Now, lets go through the steps to simplify a rational expression.
Examples of rational expressions
2
4 8 4 7, ,
3 3 5 9
x y
x x y y
![Page 16: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/16.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
![Page 17: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/17.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Would you like to review factoring of trinomials?
![Page 18: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/18.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Are the polynomials in ax2 + bx + c form?
![Page 19: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/19.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Yes, each polynomial is in ax2 + bx + c form?So for x2 + 6x + 5 we need:___ + ___ = b___ * ___ = c
![Page 20: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/20.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Yes, each polynomial is in ax2 + bx + c form?So for x2 + 6x + 5 we need:___ + ___ = 6___ * ___ = 5
![Page 21: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/21.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Yes, each polynomial is in ax2 + bx + c form?So for x2 + 6x + 5 we need:_5__ + _1__ = 6_5__ * _1__ = 5 so our numerator is
(x+5)(x+1) x2 - 25
![Page 22: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/22.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Can we factor the denominator?Do you recognize DOTS?
x2 + 6x + 5 = (x+5)(x+1) x2 - 25 x2 - 25
![Page 23: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/23.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Can we factor the denominator?Do you recognize DOTS? a2 – b2 = (a-b)(a+b)
x2 + 6x + 5 = (x+5)(x+1) x2 - 25 x2 - 25
![Page 24: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/24.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Can we factor the denominator?Do you recognize DOTS? a2 – b2 = (a-b)(a+b)So our denominator of x2 – 25 = (x - )(x + )
x2 + 6x + 5 = (x+5)(x+1) x2 - 25 x2 - 25
![Page 25: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/25.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Can we factor the denominator?Do you recognize DOTS? a2 – b2 = (a-b)(a+b)So our denominator of x2 – 25 = (x -5)(x +5 )
x2 + 6x + 5 =(x+5)(x+1) = (x+5)(x+1) x2 - 25 x2 – 25 (x-5)(x+5)
![Page 26: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/26.jpg)
Writing a rational expression in simplest form.Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
Can we cancel like binomials as like factors?Yes!Our final answer is = x+1 x-5
x2 + 6x + 5 =(x+5)(x+1) = (x+5)(x+1) x2 - 25 x2 – 25 (x-5)(x+5)
![Page 27: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/27.jpg)
Simplify: 7x 7
x2 1
Step 1: Factor the numerator and the denominator completely looking for common factors.
7x 7 7(x 1)
x2 1 (x 1)(x 1)Next
![Page 28: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/28.jpg)
7x 7
x2 1
7(x 1)
(x 1)(x 1)
What is the common factor?x 1
Step 2: Divide the numerator and denominator by the common factor.
![Page 29: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/29.jpg)
7(x 1)
(x 1)(x 1)
7(x 1)
(x 1)(x 1)
1
1
Step 3: Cancel and simplify.
Answer: 7
x 1
![Page 30: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/30.jpg)
How do I find the values that make an expression undefined?
Completely factor the original denominator.
![Page 31: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/31.jpg)
Ex: 2ab(a 2)(b 3)
3ab(a2 4)How do we determine when this is undefined? Cross out Numerator. Factor the denominator
![Page 32: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/32.jpg)
Ex: 2ab(a 2)(b 3)
3ab(a2 4)
![Page 33: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/33.jpg)
Ex: 2ab(a 2)(b 3)
3ab(a2 4)
3ab(a2 4) 3ab(a 2)(a 2)
Set factors = 0 one at a time and solve. The expression is undefined when: a= 0, 2, and -2 and b= 0. End test #2.
Factor the denominator
![Page 34: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/34.jpg)
On the Regents EXAM, “Simplest form” means all common factors have been canceled. So,
Step 1: Factor both numerator and denominator completely.
Step 2: Cancel common factors and simplify.
2
2
2
2
3 2 22
8 x x) = 1
8 6 6
( 1) 3 3) =
8 =
48 6
2 3 ( 3) =
( 2)3 2
2 =
4
1 ( 1) ( 1) =
1( 1) 2 2
) Already in lowest terms
( 1)) = 1 1
( 11 ) 1
xA
x
x x xB
x x x
C
xD x
x x
x
x x x
x
xx
x x
y
y
x x x x x
x
![Page 35: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/35.jpg)
Lets go through another example. Put this expression in simplest form.
3a3 a4
2a3 6a2
3a3 a4
2a3 6a2 a3 (3 a)
2a2 (a 3)
Factor out the GCF
Next
![Page 36: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/36.jpg)
3
22 ( 3)
(3 )a
a a
a
3 factored is 1( 3)a a
cancel like factors3
2
1 ( 3)
2 ( 3)
a a
a a
1
1
3
2
1( 3)
2 ( 3)
a
a a
a
KEY TRICK
![Page 37: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/37.jpg)
3
2
1
2
a
a
2cancel out the like factor a
1
2
a1
a
answer
For what values will the original expression be undefined? Go back to prior slide and set factors = 0.
![Page 38: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/38.jpg)
Now try to do some on your own.
Put these in their simplest form.
2
2
3 2
3 2
5 61)
9
5 102)
6 16
x x
x
x x
x x x
Also find the values that make each expression undefined? Time permitting start hwk.
![Page 39: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/39.jpg)
Multiplying Rational Expressions. With rational expressions, we always factor first and then cancel common factors in numerators and denominators before we multiply.
Ex: 4a2
5ab3 3bc
12a3 4 a a 3 bc
5 a b b b 12 a a a
11 1 1 1
1 1 1 1
c
5b2 a2
![Page 40: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/40.jpg)
Let’s do another one.
Ex: x3 3x2
x2 5x 6
x2 10x 9
x2 6x 27Step #1: Factor the numerator and the denominator.
x2 (x 3)
(x 6)(x 1)(x 1)(x 9)
(x 9)(x 3)Next
![Page 41: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/41.jpg)
Step #2: Divide the numerator and denominator by the common factors.
x2 (x 3)
(x 6)(x 1)(x 1)(x 9)
(x 9)(x 3)1
1
1
1
1
1
![Page 42: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/42.jpg)
Step #3: Multiply the numerator and the denominator.
x2
x 6
Next: division of rational expressions.
![Page 43: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/43.jpg)
Recall how to divide by a fraction:
Multiply by the reciprocal of the divisor.
4
5
16
25
4
5
25
16
4 25
516
1
1
5
4
5
4
AKA: Keep Flip Change
![Page 44: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/44.jpg)
Ex: Simplifyy 2
y2 10 y 24
y2 2y
y2 2y 8
![Page 45: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/45.jpg)
y 2
y2 10 y 24
y2 2y
y2 2y 8
y 2
y2 10 y 24y2 2y 8
y2 2y
y 2
(y 12)(y 2)(y 4)(y 2)
y(y 2)
1 1
1 1
Next
4
( 12)
y
y y
Keep - Flip - Change
![Page 46: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/46.jpg)
Now you try to simplify the expression:
x 3
x2 4x 12
2x2 6x
x 2
Keep - Flip - Change
![Page 47: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/47.jpg)
Answer: 1
2x(x 6)Now try these on your own.Keep - Flip - Change
1) x + 3
2x3 2x2
x2 7x 6
x2 10x 21
2) 3x 67x 7
5x 1014x 14
![Page 48: 21(x * x *x) ÷ 7 (x*x) Otcq. Aim 2-1: How do we define and simplify rational expressions? HWk read 2-1 p 67# 1-10 Objective: SWBAT Simplify a Rational.](https://reader034.fdocuments.in/reader034/viewer/2022051620/56649e935503460f94b98dc0/html5/thumbnails/48.jpg)
Here are the answers:
1) x 6
2x2 (x 7)
2) 6(x 1)5(x 1)