Back to Perform rational expression operations — Problem 3 · 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

To add $\dfrac{1}{x - 2} + \dfrac{1}{x + 3}$ , which is the correct LCD and the correctly built equivalent fractions?

LCD $= (x-2)(x+3)$ ; rewrite as $\dfrac{x+3}{(x-2)(x+3)} + \dfrac{x-2}{(x-2)(x+3)}$

LCD $= (x-2) + (x+3) = 2x+1$ ; rewrite as $\dfrac{1}{2x+1} + \dfrac{1}{2x+1}$

LCD $= (x-2)(x+3)$ ; rewrite as $\dfrac{1}{(x-2)(x+3)} + \dfrac{1}{(x-2)(x+3)}$

LCD $= (x-2)^2(x+3)^2$ ; rewrite as $\dfrac{(x+3)^2}{(x-2)^2(x+3)^2} + \dfrac{(x-2)^2}{(x-2)^2(x+3)^2}$