Simplify ((8x^2+24x)/(x^2-9))/((2x)/(15-5x))

$\frac{\frac{8 x^{2} + 24 x}{x^{2} - 9}}{\frac{2 x}{15 - 5 x}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 x^{2} + 24 x}{x^{2} - 9} \cdot \frac{15 - 5 x}{2 x}$

Factor $8 x$ out of $8 x^{2} + 24 x$ .

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

$\frac{8 x (x) + 24 x}{x^{2} - 9} \cdot \frac{15 - 5 x}{2 x}$

Factor $8 x$ out of $24 x$ .

$\frac{8 x (x) + 8 x (3)}{x^{2} - 9} \cdot \frac{15 - 5 x}{2 x}$

Factor $8 x$ out of $8 x (x) + 8 x (3)$ .

$\frac{8 x (x + 3)}{x^{2} - 9} \cdot \frac{15 - 5 x}{2 x}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{8 x (x + 3)}{x^{2} - 3^{2}} \cdot \frac{15 - 5 x}{2 x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{8 x (x + 3)}{(x + 3) (x - 3)} \cdot \frac{15 - 5 x}{2 x}$

Simplify terms.

Cancel the common factor of $2 x$ .

Factor $2 x$ out of $8 x (x + 3)$ .

$\frac{2 x (4 (x + 3))}{(x + 3) (x - 3)} \cdot \frac{15 - 5 x}{2 x}$

Cancel the common factor.

$\frac{2 x (4 (x + 3))}{(x + 3) (x - 3)} \cdot \frac{15 - 5 x}{2 x}$

Rewrite the expression.

$\frac{4 (x + 3)}{(x + 3) (x - 3)} (15 - 5 x)$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{4 (x + 3)}{(x + 3) (x - 3)} (15 - 5 x)$

Rewrite the expression.

$\frac{4}{x - 3} (15 - 5 x)$

Multiply $\frac{4}{x - 3}$ by $15 - 5 x$ .

$\frac{4 (15 - 5 x)}{x - 3}$

Simplify the numerator.

Factor $5$ out of $15 - 5 x$ .

Factor $5$ out of $15$ .

$\frac{4 (5 (3) - 5 x)}{x - 3}$

Factor $5$ out of $- 5 x$ .

$\frac{4 (5 (3) + 5 (- x))}{x - 3}$

Factor $5$ out of $5 (3) + 5 (- x)$ .

$\frac{4 (5 (3 - x))}{x - 3}$

$\frac{4 \cdot 5 (3 - x)}{x - 3}$

Multiply $4$ by $5$ .

$\frac{20 (3 - x)}{x - 3}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3 - x$ and $x - 3$ .

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{20 (- 1 (- 3) - x)}{x - 3}$

Factor $- 1$ out of $- x$ .

$\frac{20 (- 1 (- 3) - (x))}{x - 3}$

Factor $- 1$ out of $- 1 (- 3) - (x)$ .

$\frac{20 (- 1 (- 3 + x))}{x - 3}$

Reorder terms.

$\frac{20 (- 1 (x - 3))}{x - 3}$

Cancel the common factor.

$\frac{20 (- 1 (x - 3))}{x - 3}$

Divide $20 \cdot (- 1)$ by $1$ .

$20 \cdot (- 1)$

Multiply $20$ by $- 1$ .

$- 20$

Simplify ((8x^2+24x)/(x^2-9))/((2x)/(15-5x))

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