Precalc hw #3 Rational Expressions - Mrs. Sevilla's Math...
Transcript of Precalc hw #3 Rational Expressions - Mrs. Sevilla's Math...
Main Ideas/Questions Notes/Examples
Rational Expressions
• A rational expression is a _____________________ of two polynomial expressions.
• Recall:
x + yy + x
=1 and
x − yy − x
= −1
Simplifying Expressions
Factor & Cancel
1.
64k 3 −14k2 −13k + 3
2.
12n2 − 48n288n2 −18n4
Multiplying & Dividing
Expressions
For Multiplication:
Factor, then simplify.
For Division: Multiply by the
reciprocal.
3.
x2 −10x − 24x3 + 2x2
⋅ 5x2 − 20xx2 −16x + 48
4.
5 p2 + 29p −65 p2 − 26 p + 5
⋅ 3 p2 −15 p36 − p2
5.
6s2 +11s + 41− 4s2
÷ 2s2 − s −12s2 − 3s +1
6.
k 4 −162k2 − k −6
÷ 4k 3 +16k12k2 +18k
Adding & subtracting Expressions
Get common denominators,
combine, then simplify
7.
34w
− 25w
8.
2x −1x + 4
− 3
Name: ___________________________________________________
Class: _________________________________
Date: _________________________________
Topic: ___________________________________________________
x y
© Gina Wilson (All Things Algebra®, LLC), 2017
9.
r + 5r2 − 25
+ 6r − 5
10.
5a +6a2 − 4
− 1a + 2
11.
q +1q − 4
− q −1q2 −7q +12
12.
3x +6
− 2x −1
Complex fractions
Combine the
numerator and denominator into a
single fraction, multiply by the reciprocal,
then simplify.
13.
110
− 940r2
13− 1
2r
14.
3 2
2 61
13
y y
y
+
+
15.
2
2
2
45 101 1
2
m nn m
n mn
+
+
© Gina Wilson (All Things Algebra®, LLC), 2017
Name: ___________________________________ Unit 1: Fundamental Skills
Date: ________________________ Per: ______ Homework 3: Rational Expressions
Directions: Simplify each expression.
1. 2
4 2
2 24 4x xx x
−−
2. 2
2
2036 9a aa a+ −−
3.
2k2 − 5k − 3k 3 − 27
Directions: Find each product or quotient. Give your answer in simplest form.
4. 2 2
3 2 2
2 24 36 12
x x x xx x x x+ − +⋅+ − −
5. 2
2 2
4 11 3 8 216 1 9w w ww w− − −⋅
− −
6. 2
4 2
1 11 1
c cc c
− +÷− +
7. 2 2
2 2
2 3 8 122 7 15 25m m m m
m m m+ +÷
− − −
Directions: Find each sum or difference. Give your answer in simplest form.
8. 2
1 36 4a a
− 9. 1
23
xx+−−
** This is a 2-page document! **
© Gina Wilson (All Things Algebra®, LLC), 2017
10. 2
3 2 324 16
pp p
+++ −
11.
n2 + 7n −18n2 − 5n + 6
− 1n − 3
12. 2 17 4y y+
− − 13.
2 2
19 8 15
rr r r
−− + +
Directions: Simplify each complex fraction.
14.
2
14
8 2k
k k
−
− 15.
329
4
v
vv
+
−
16.
2
29 2
13 2
a bb aab b
−
+ 17.
2
2
1
14( )
xx
xx
+
+
18. Write an expression to represent the area of the rectangle below in simplest form.
© Gina Wilson (All Things Algebra®, LLC), 2017