Back to Perform rational expression operations — Problem 2 · Task Set 22

Exercises: Rational Expression Arithmetic (Add, Subtract, Multiply, Divide)

This is an advanced (+) topic. Work through each section in order. Factor all numerators and denominators before multiplying or dividing. State domain restrictions for all problems.

Grade 10·19 problems·~45 min·Common Core Math - HS Algebra·standard·hsa-apr-d-7

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Recall / Warm-Up

Which integer arithmetic rule directly parallels the rational expression rule $\dfrac{a(x)}{b(x)} + \dfrac{c(x)}{b(x)} = \dfrac{a(x) + c(x)}{b(x)}$ ?

$\dfrac{3}{7} + \dfrac{2}{7} = \dfrac{3 + 2}{7} = \dfrac{5}{7}$

$\dfrac{3}{7} + \dfrac{2}{5} = \dfrac{3 + 2}{7 + 5} = \dfrac{5}{12}$

$\dfrac{3}{7} \times \dfrac{2}{7} = \dfrac{3 \times 2}{7 \times 7} = \dfrac{6}{49}$

$\dfrac{3}{7} \div \dfrac{2}{7} = \dfrac{3}{7} \times \dfrac{7}{2} = \dfrac{3}{2}$