H. Algebra 2
9.2 Notes
9.2 Multiplying and Dividing Rational Expressions
Date: _______________
EXPLORE: Relating Multiplication Concepts
Multiply
4 5
∙
5 6
, and simplify the product.
Based on the steps you took to multiply rational numbers, how might you multiply the rational
𝑥+1
3
expressions 𝑥−1 ∙ 2(𝑥+1)?
Discussion. Multiplying rational expressions is similar to multiplying rational numbers. Likewise,
____________________ rational expressions is similar to dividing rational numbers. How could you use the
steps for dividing rational numbers to divide rational expressions?
Multiplying Rational Expressions
Learning Target E: I can multiply rational expressions.
Find the products and any excluded values.
A)
3𝑥 2
𝑥 2 −2𝑥−8
∙
2𝑥 2 −6𝑥−20
𝑥 2 −3𝑥−10
B)
𝑥 2 −8𝑥
14(𝑥 2 +8𝑥+15)
∙
7𝑥+35
𝑥+8
1
H. Algebra 2
C)
9.2 Notes
𝑥 2 −9
𝑥 2 −5𝑥−24
∙
𝑥−8
D)
2𝑥 2 −18𝑥
𝑥
𝑥−9
∙
3𝑥−27
𝑥+1
Dividing Rational Expressions
Learning Target F: I can divide rational expressions.
Find each quotient and any excluded values.
A)
C)
(𝑥+7)2
𝑥2
𝑥+11
4𝑥
÷
÷
𝑥 2 +9𝑥+14
𝑥 2 +𝑥−2
2𝑥+6
𝑥 2 +2𝑥−3
B)
D)
6𝑥
3𝑥−30
20
𝑥 2 −7𝑥
÷
÷
9𝑥 2 −27𝑥−36
𝑥 2 −10𝑥
5𝑥 2 −40𝑥
𝑥 2 −15𝑥+56
2
H. Algebra 2
9.2 Notes
Activity: Investigating Closure
A set of numbers is said to be closed, or to have closure, under a given operation if the result of the
operation on any two numbers in the set is also in the set.
Recall whether the set of whole numbers, the set of integers, and the set of rational numbers
are closed under each of the four basic operations.
Addition
Subtraction
Multiplication
Division
Whole Numbers
Integers
Rational Numbers
Look at the set of rational expressions. Use the rational expressions
𝑝(𝑥)
𝑞(𝑥)
and
𝑟(𝑥)
𝑠(𝑥)
where p(x), q(x),
r(x), and s(x) are nonzero. Add, subtract, multiply, and divide the rational expressions to determine
which operations rational expressions have closure.
Addition:
𝑝(𝑥)
𝑞(𝑥)
Multiplication:
+
𝑟(𝑥)
𝑠(𝑥)
𝑝(𝑥)
𝑞(𝑥)
=
∙
𝑟(𝑥)
𝑠(𝑥)
𝑝(𝑥)
Subtraction:
=
Division:
𝑞(𝑥)
𝑝(𝑥)
𝑞(𝑥)
÷
𝑟(𝑥)
𝑠(𝑥)
−
𝑟(𝑥)
𝑠(𝑥)
=
=
Reflect. Are rational expressions most like whole number, integers, or rational numbers?
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