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## Get ready for AP® Calculus

### Course: Get ready for AP® Calculus>Unit 1

Lesson 22: Multiplying and dividing rational expressions

# Multiply & divide rational expressions: Error analysis

## Problem

Rutendo tried to perform the following multiplication and reduce to lowest terms:
$\frac{-3x+15}{2x+16}\cdot \frac{x-7}{{x}^{2}-25}$
This is his work:
Rewriting the first factor: $\frac{-3x+15}{2x+16}=\frac{-3\left(x+5\right)}{2\left(x+8\right)}$
Rewriting the second factor: $\frac{x-7}{{x}^{2}-25}=\frac{x-7}{\left(x+5\right)\left(x-5\right)}$
Finding excluded values: $x\ne ±5$ and $x\ne -8$
Multiplying and reducing to lowest terms:
$\begin{array}{rl}& \phantom{=}\frac{-3x+15}{2x+16}\cdot \frac{x-7}{{x}^{2}-25}\\ \\ & =\frac{-3\left(x+5\right)}{2\left(x+8\right)}\cdot \frac{x-7}{\left(x+5\right)\left(x-5\right)}\\ \\ & =\frac{-3\overline{)\left(x+5\right)}\left(x-7\right)}{2\left(x+8\right)\overline{)\left(x+5\right)}\left(x-5\right)}\\ \\ & =\frac{-3\left(x-7\right)}{2\left(x+8\right)\left(x-5\right)}\end{array}$
What mistake did Rutendo make?