Lesson 22
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA II
Name: _______________________________________________ Alg1 CC HW M1 L 22 -- VISCA
Problem Set
1.
Find an equivalent rational expression in lowest terms, and identify the value(s) of the variable that must be
excluded to prevent division by zero.
a.
b.
c.
d.
e.
f.
g.
h.
2.
𝑦−𝑥
i.
20𝑛
𝑥3𝑦
𝑥−𝑦
𝑎2 −𝑏 2
j.
𝑦4𝑥
2𝑛−8𝑛2
𝑏+𝑎
k.
4𝑛
𝑑𝑏+𝑑𝑐
𝑥 2 −9𝑏 2
(𝑥−3)3
m.
𝑥 2 −2𝑥𝑏−3𝑏 2
3𝑛2 −5𝑛−2
n.
2𝑛−4
3𝑥−2𝑦
o.
9𝑥 2 −4𝑦 2
4𝑎2 −12𝑎𝑏
p.
𝑎2 −6𝑎𝑏+9𝑏 2
3𝑦−6𝑥
9−𝑥 2
l.
𝑑𝑏
4𝑥−2𝑦
𝑥 2 −5𝑥+6
8−2𝑥−𝑥 2
𝑎−𝑏
𝑥𝑎−𝑥𝑏−𝑎+𝑏
(𝑥+𝑦)2 −9𝑎2
2𝑥+2𝑦−6𝑎
8𝑥 3 −𝑦 3
4𝑥 2 −𝑦 2
Write a rational expression with denominator 6𝑏 that is equivalent to
a.
b.
c.
3.
16𝑛
𝑎
𝑏
.
𝑎
one-half of .
𝑏
1
3
.
Remember that algebra is just another way to perform arithmetic, but with variables replacing numbers.
2
(𝑥 2 𝑦) (𝑥𝑦)3 𝑧 2
a.
Simplify the following rational expression:
b.
Simplify the following rational expression without using a calculator:
c.
How are the calculations in parts (a) and (b) similar? How are they different? Which expression was easier to
(𝑥𝑦 2 )2 𝑦𝑧
.
122 ∙63 ∙52
182 ∙15
.
simplify?
Lesson 22:
Date:
Equivalent Rational Expressions
3/19/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.106
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 22
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA II
Name: _______________________________________________ Alg1 CC HW M1 L 22 -- VISCA
REVIEW:
4. Evaluate: (4x3 + 2x2 - 11x + 8) ÷ (x – 3)
5. Is (x + 2) a factor of (5x4 + 10x3 – 7x2 – 20x – 12)?
6. What is the remainder when (12x3 – 8x2 + 9) is divided by (2x + 4)?
7. Figure out the function for the graph below:
Lesson 22:
Date:
Equivalent Rational Expressions
3/19/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.107
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.