Answer
$\frac{x + 4}{x - 5}$
Work Step by Step
To divide two expressions, we multiply the first one with the reciprocal of the second one:
$\frac{(x + 4)(x + 5)}{(x - 5)(x + 2)} • \frac{(x + 2)(x - 7)}{(x + 5)(x - 7)}$
Now, we want to cancel out the factors that are common in the numerators and denominators of each rational expression:
$\frac{(x + 4)(x + 5)}{(x - 5)(x + 2)} • \frac{x + 2}{x + 5}$
To multiply two expressions, we multiply the two expressions together:
$\frac{(x + 4)(x + 5)(x + 2)}{(x - 5)(x + 2)(x + 5)}$
Cancel out factors that are common in the numerator and denominator:
$\frac{x + 4}{x - 5}$
