Answer
$ \displaystyle \frac{(x-1)(x+7)}{x-5}$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ = multiplying with $\displaystyle \frac{Q}{P}$
Rewrite the problem:
$ \displaystyle \frac{x^{2}+4x-5}{1}\cdot\frac{x+7}{x^{2}-25}=\qquad$ ... factor what we can
... $x^{2}+4x-5=$... factors of $-5$ whose sum is $+4$ ... are $+5$ and $-1$
$=(x+5)(x-1)$
... $x^{2}-25$= difference of squares = $(x+5)(x-5)$
Rewrite the problem:
$ \displaystyle \frac{(x+5)(x-1)}{1}\cdot\frac{(x+7)}{(x+5)(x-5)}=\qquad$ ... ... reduce common factors
= $ \displaystyle \frac{(1)(x-1)}{1}\cdot\frac{(x+7)}{(1)(x-5)}=$
= $ \displaystyle \frac{(x-1)(x+7)}{x-5}$
