Question

perform the following operation and express in simplest form.
$\frac{x^{2}+15x+56}{x} div \frac{x^{2}+2x-35}{4x-20}$

Explanation:

Step1: Rewrite division as multiplication

$\frac{x^2 + 15x + 56}{x} \times \frac{4x - 20}{x^2 + 2x - 35}$

Step2: Factor all polynomials

$\frac{(x+7)(x+8)}{x} \times \frac{4(x-5)}{(x+7)(x-5)}$

Step3: Cancel common factors

Cancel $(x+7)$ and $(x-5)$:
$\frac{(x+8)}{x} \times \frac{4}{1}$

Step4: Multiply remaining terms

$\frac{4(x+8)}{x}$

Answer:

$\frac{4x + 32}{x}$ or $4 + \frac{32}{x}$