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# Multiply & divide rational expressions: Error analysis

## Problem

Rutendo tried to perform the following multiplication and reduce to lowest terms:
start color #0c7f99, start fraction, minus, 3, x, plus, 15, divided by, 2, x, plus, 16, end fraction, end color #0c7f99, dot, start color #9e034e, start fraction, x, minus, 7, divided by, x, squared, minus, 25, end fraction, end color #9e034e
This is his work:
Rewriting the first factor: start color #0c7f99, start fraction, minus, 3, x, plus, 15, divided by, 2, x, plus, 16, end fraction, end color #0c7f99, equals, start fraction, minus, 3, left parenthesis, x, plus, 5, right parenthesis, divided by, 2, left parenthesis, x, plus, 8, right parenthesis, end fraction
Rewriting the second factor: start color #9e034e, start fraction, x, minus, 7, divided by, x, squared, minus, 25, end fraction, end color #9e034e, equals, start fraction, x, minus, 7, divided by, left parenthesis, x, plus, 5, right parenthesis, left parenthesis, x, minus, 5, right parenthesis, end fraction
Finding excluded values: x, does not equal, plus minus, 5 and x, does not equal, minus, 8
Multiplying and reducing to lowest terms:
\begin{aligned} &\phantom{=}\blueE{\dfrac{-3x+15}{2x+16}} \cdot \maroonE{\dfrac{x-7}{x^2-25}} \\\\ &=\dfrac{-3(x+5)}{2(x+8)}\cdot\dfrac{x-7}{(x+5)(x-5)} \\\\ &=\dfrac{-3\cancel{(x+5)}(x-7)}{2(x+8)\cancel{(x+5)}(x-5)} \\\\ &=\dfrac{-3(x-7)}{2(x+8)(x-5)} \end{aligned}
What mistake did Rutendo make?