Question

$\frac{3x^{2}+15x}{x^{2}-3x-40} div \frac{5x^{2}}{x^{2}-64}$

Explanation:

Step1: Rewrite division as multiplication

$\frac{3x^2 + 15x}{x^2 - 3x - 40} \times \frac{x^2 - 64}{5x^2}$

Step2: Factor all expressions

Factor numerator/denominator:
$3x^2+15x=3x(x+5)$
$x^2-3x-40=(x-8)(x+5)$
$x^2-64=(x-8)(x+8)$
Substitute:
$\frac{3x(x+5)}{(x-8)(x+5)} \times \frac{(x-8)(x+8)}{5x^2}$

Step3: Cancel common factors

Cancel $(x+5)$, $(x-8)$, $x$:
$\frac{3}{1} \times \frac{(x+8)}{5x}$

Step4: Multiply remaining terms

$\frac{3(x+8)}{5x}$

Answer:

$\frac{3(x+8)}{5x}$ (or $\frac{3x+24}{5x}$)