Simplify ((8x^2)/(x+4))÷(x/(2(x-4)))

$\frac{8 x^{2}}{x + 4} \div \frac{x}{2 (x - 4)}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 x^{2}}{x + 4} \cdot \frac{2 (x - 4)}{x}$

Step 2

Cancel the common factor of $x$ .

Factor $x$ out of $8 x^{2}$ .

$\frac{x (8 x)}{x + 4} \cdot \frac{2 (x - 4)}{x}$

Cancel the common factor.

$\frac{x (8 x)}{x + 4} \cdot \frac{2 (x - 4)}{x}$

Rewrite the expression.

$\frac{8 x}{x + 4} (2 (x - 4))$

Step 3

Combine $2$ and $\frac{8 x}{x + 4}$ .

$\frac{2 (8 x)}{x + 4} (x - 4)$

Step 4

Multiply $8$ by $2$ .

$\frac{16 x}{x + 4} (x - 4)$

Step 5

Multiply $\frac{16 x}{x + 4}$ by $x - 4$ .

$\frac{16 x (x - 4)}{x + 4}$