1. Dividing Rational Expressions

2. Division of Rational Expressions
Change the operation to multiplication, write the reciprocal of the second fraction
4𝑥 16 𝑦 2 ∙ 𝟖 𝒚 𝟑 𝟓 𝒙 𝟕 𝒚 𝟑
𝑥 4 𝑦 2 ∙ 8 5 𝑥 7
Simplify the fractions individually
8𝑥 20 𝑦 2 𝑥 7
Multiply the numerators and denominators
𝟐 𝟓 𝒚 𝟐 𝒙 𝟔
Simplify the final fraction

3. Dividing Practice
Complete #10 and 11 on the practice half sheet on a separate sheet of paper
An answer key is available on the front table for you to check

4. Additional Division Example – this example is not in your notes, copy onto the blank back page of your packet
5𝑥 3𝑥−12 ÷ 𝑥 2 −2𝑥 𝑥 2 −6𝑥+8
5𝑥 3𝑥−12 ∙ 𝑥 2 −6𝑥+8 𝑥 2 −2𝑥
Change the operation to multiplication, write the reciprocal of the second fraction
5𝑥 3(𝑥−4) ∙ (𝑥−4)(𝑥−2) 𝑥(𝑥−2)
factor
Simplify fractions individually
5𝑥(𝑥−4) 3𝑥(𝑥−4)
Multiply across and reorder factors
5 3
Simplify again

5. Dividing Practice
Complete #9 and 13 on the practice half sheet on a separate sheet of paper
An answer key is available on the front table for you to check

6. Complex Fraction Example – this example is not in your notes, copy onto the blank back page of your packet
Complex fractions are fractions that have numerators and/or denominators that are also fractions
2 𝑥 2 −12𝑥 𝑥 2 −7𝑥+6 2𝑥 3𝑥−3
Numerator fraction
denominator fraction
2 𝑥 2 −12𝑥 𝑥 2 −7𝑥+6 ÷ 2𝑥 3𝑥−3
Rewrite as a division problem
Change to multiplication, write reciprocal of second fraction
2 𝑥 2 −12𝑥 𝑥 2 −7𝑥+6 ∙ 3𝑥−3 2𝑥
2𝑥(𝑥−6) (𝑥−6)(𝑥−1) ∙ 3(𝑥−1) 2𝑥
Factor
Simplify individual fractions
6𝑥(𝑥−1) 2𝑥(𝑥−1)
Multiply, and reorder factors
Simplify to get final answer 3

7. Dividing Practice
Complete #12 and 14 on the practice half sheet on a separate sheet of paper
An answer key is available on the front table for you to check