Question

multiply
\\(\frac{x - 4}{5x + 25} \cdot \frac{2x + 10}{2x - 8}\\)

select the correct choice below and fill in the answer box(es) to complete your choice.
(simplify your answer. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)
\\(\boldsymbol{\circ}\\) a. \\(\frac{x - 4}{5x + 25} \cdot \frac{2x + 10}{2x - 8} = \frac{1}{2}, x \
eq 4\\)
\\(\boldsymbol{\circ}\\) b. \\(\frac{x - 4}{5x + 25} \cdot \frac{2x + 10}{2x - 8} = \square\\), no numbers must be excluded

Explanation:

Step1: Factor all polynomials

$\frac{x-4}{5(x+5)} \cdot \frac{2(x+5)}{2(x-4)}$

Step2: Cancel common factors

$\frac{\cancel{x-4}}{5\cancel{(x+5)}} \cdot \frac{\cancel{2}\cancel{(x+5)}}{\cancel{2}\cancel{(x-4)}} = \frac{1}{5}$

Step3: Find excluded values

Denominators cannot be 0:
$5x+25=0 \implies x=-5$
$2x-8=0 \implies x=4$
So $x
eq -5, 4$

Answer:

A. $\frac{x-4}{5x+25} \cdot \frac{2x+10}{2x-8} = \frac{1}{5}$, $x
eq -5, 4$