Answer
$\frac{x + 4}{x + 2}$
Work Step by Step
To divide two expressions, we multiply the first one with the reciprocal of the second one:
$\frac{(x + 3)(x + 5)}{(x - 7)(x + 3)} • \frac{(x + 4)(x - 7)}{(x + 5)(x + 2)}$
Let's cancel out common factors in the numerator and denominator:
$\frac{x + 5}{(x - 7)(x + 3)} • \frac{(x + 4)(x - 7)}{(x + 5)(x + 2)}$
When multiplying two rational expressions, we combine the two expressions together into one by multiplying the numerators together and multiplying the denominators together:
$\frac{(x + 5)(x + 4)(x - 7)}{(x - 7)(x + 5)(x + 2)}$
We can cancel out the common factors in the numerator and denominator:
$\frac{x + 4}{x + 2}$
