Multiply and Divide Rational...
Transcript of Multiply and Divide Rational...
Multiply and Divide
Rational ExpressionsLESSON 6.1
Objective
Determine the domain of rational
expressions and functions
Simplify, multiply, and divide rational
expressions and functions
Rational Expressions
A rational expression is the quotient (÷) of
two polynomials
EX: 𝑥−5
2𝑥+1
𝑥2−7𝑥−18
𝑥2−4
1
𝑥−3
2𝑎2+5𝑎𝑏+2𝑏2
𝑎2−6𝑎𝑏+8𝑏2
Rational Expressions - Domain
REMEMBER: We cannot ÷0
Domain consists of all real numbers
except those for which the denominator
is zero.
Rational Expressions - Domain
Determine the domain for each of the
following rational expressions
A. −3𝑧
𝑧+5B.
𝑛2−2𝑛−8
𝑛2−𝑛−12
Rational Expressions - Domain
Determine the domain for each of the
following rational expressions
C. 𝑅 𝑥 =𝑥−3
𝑥2−2𝑥−8
Rational Expressions - Simplify
Rational expressions can be simplified by
dividing out any common factors
EX: 10
10= 1
𝑥
𝑥= 1
𝑥−3
𝑥−3= 1
2 𝑥−3
3(𝑥−3)=
2
3
Rational Expressions - Simplify
Simplify
D. 𝑥2+𝑥−6
2𝑥2−5𝑥+2E.
𝑦3+27
2𝑦2+6𝑦
Rational Expressions - Multiply
MULTIPLYING RATIONAL EXPRESSIONS
1. Completely factor each polynomial
2. Divide out common factors
3. Multiply remaining terms (fractions)
Rational Expressions - Multiply
F. 𝑛2−9
𝑛2+5𝑛+6×
𝑛+2
−2𝑛+6
Rational Expressions - Multiply
G. 𝑎2−𝑏2
10𝑎2−10𝑎𝑏×
10𝑎+5𝑏
2𝑎2+3𝑎𝑏+𝑏2
Rational Expressions - Divide
DIVIDING RATIONAL EXPRESSIONS𝑎𝑏𝑐𝑑
=𝑎
𝑏÷𝑐
𝑑=𝑎
𝑏×𝑑
𝑐
KFC→Keep the First, Flip the Second, Change the Sign
Rational Expressions - Divide
H.
45𝑧4
7𝑦5𝑧
21𝑦2
Rational Expressions - Divide
I.
𝑝3−8
5𝑝2+15𝑝
𝑝2−4
𝑝2+3𝑝
Rational Expressions - Functions
Sometimes we are given two or more
functions and told to combine and
simplify them.
EX: 𝑓 𝑥
𝑔 𝑥𝑓 𝑥 ⋅ 𝑔(𝑥)
Rational Expressions - Functions
J. 𝑓 𝑥 =𝑥2−9
2𝑥2−8𝑥𝑔 𝑥 =
𝑥−4
𝑥2+4𝑥+3ℎ 𝑥 =
𝑥2+6𝑥+9
𝑥2−5𝑥
1. Find 𝑓 𝑥 ⋅ 𝑔(𝑥)
2. Find 𝑓 𝑥
ℎ 𝑥