Multiply & divide rational expressions: Error analysis

Rutendo tried to perform the following multiplication and reduce to lowest terms:

\frac{- 3 x + 15}{2 x + 16} \cdot \frac{x - 7}{x^{2} - 25}

This is his work:

Rewriting the first factor: $\frac{- 3 x + 15}{2 x + 16} = \frac{- 3 (x + 5)}{2 (x + 8)}$ ‍

Rewriting the second factor: $\frac{x - 7}{x^{2} - 25} = \frac{x - 7}{(x + 5) (x - 5)}$ ‍

Finding excluded values: $x \neq \pm 5$ ‍ and $x \neq - 8$ ‍

Multiplying and reducing to lowest terms:

$\begin{aligned} \frac{- 3 x + 15}{2 x + 16} \cdot \frac{x - 7}{x^{2} - 25} \\ = \frac{- 3 (x + 5)}{2 (x + 8)} \cdot \frac{x - 7}{(x + 5) (x - 5)} \\ = \frac{- 3 (x + 5) (x - 7)}{2 (x + 8) (x + 5) (x - 5)} \\ = \frac{- 3 (x - 7)}{2 (x + 8) (x - 5)} \end{aligned}$ ‍

What mistake did Rutendo make?

(Choice A)
He excluded $x = - 5$ ‍, which doesn't make the final expression undefined.
(Choice B)
He didn't exclude $x = 7$ ‍, which makes the numerator of the second factor equal to zero.
(Choice C)
He didn't rewrite the first factor correctly.
(Choice D)
He didn't rewrite the second factor correctly.

Precalculus

Course: Precalculus > Unit 4

Problem