Dividing Rational Expressions

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

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

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

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

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

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