Question

question #15
which of the following would be the first step in writing the rational expression in simplest form?
\\(\frac{2x + 10}{5x - 25}\div\frac{9}{6x - 30}\\)
\\(\circ\frac{2(x + 5)}{5(x - 5)}cdot\frac{6(x - 5)}{9}\\\circ\frac{4(x + 5)}{15}\\\circ\frac{2(x + 5)}{5}cdot\frac{2}{3}\\\circ already in simplest form

Explanation:

Step1: Factor out common factors

Factor $2x + 10$ to $2(x + 5)$, $5x-25$ to $5(x - 5)$, $6x - 30$ to $6(x - 5)$. Then rewrite division as multiplication by reciprocal: $\frac{2x + 10}{5x-25}\div\frac{9}{6x - 30}=\frac{2(x + 5)}{5(x - 5)}\times\frac{6(x - 5)}{9}$.

Answer:

A. $\frac{2(x + 5)}{5(x - 5)}\cdot\frac{6(x - 5)}{9}$