Section 5.2
Rational Expressions: Multiplying and Dividing Rational Expressions
Recall: Multiplying fractions
1) Factor into primes 2) Cancel common factors. 3) Multiply across.
10 14
∙
= 21 8
Now, when Muliplying Rational Expressions we use the same three steps on the polynomials.
1) FACTOR each polynomial in the numerator and denominator into primes.
2) Cancel all common FACTORS that are common between the numerator and denominator.
Category Rules for Canceling:
Monomials: factors only cancel with other monomial factors as discussed in Section 0.4
Binomials: factors only cancel with other identical binomial factors
(opposites cancel and leave behind a “-1”)
Trinomials: factors only cancel with other identical trinomial factors
3) Multiply across.
Recall: Dividing fractions
1) Flip the second fraction. 2) Factor into primes 3) Cancel common factors. 4) Multiply across.
10 8
÷
= 21 14
Now, when Dividing Rational Expressions we use the same four steps on the polynomials.
1) Flip the second fraction and change the operation to multiplication.
2) FACTOR each polynomial in the numerator and denominator into primes.
3) Cancel all common FACTORS that are common between the numerator and denominator.
Category Rules for Canceling:
Monomials: factors only cancel with other monomial factors as discussed in Section 0.4
Binomials: factors only cancel with other identical binomial factors
(opposites cancel and leave behind a “-1”)
Trinomials: factors only cancel with other identical trinomial factors
4) Multiply across.
Example: Perform the indicated operations. Make sure your answer is reduced to lowest terms.
÷
a)
b)
∙
𝑐) 𝑥 + 3𝑥 − 4𝑥 − 12 8𝑥 + 24
∙ 4𝑥 + 8𝑥
9−𝑥
𝑑) 𝑥 −𝑥
10𝑥 − 10𝑥
∙
5𝑥 − 5𝑥 2𝑥 + 2𝑥 + 2𝑥
e)
÷
f)
÷