Simplify ((x^2-9)/4)/((3-x)/8)

$\frac{\frac{x^{2} - 9}{4}}{\frac{3 - x}{8}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 9}{4} \cdot \frac{8}{3 - x}$

Simplify terms.

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{x^{2} - 9}{4} \cdot \frac{4 (2)}{3 - x}$

Cancel the common factor.

$\frac{x^{2} - 9}{4} \cdot \frac{4 \cdot 2}{3 - x}$

Rewrite the expression.

$(x^{2} - 9) \frac{2}{3 - x}$

Multiply $x^{2} - 9$ by $\frac{2}{3 - x}$ .

$\frac{(x^{2} - 9) \cdot 2}{3 - x}$

Simplify the numerator.

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

$\frac{(x^{2} - 3^{2}) \cdot 2}{3 - x}$

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 $b = 3$ .

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

Simplify terms.

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

Factor $- 1$ out of $x$ .

$\frac{(x + 3) (- 1 (- x) - 3) \cdot 2}{3 - x}$

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

$\frac{(x + 3) (- 1 (- x) - 1 (3)) \cdot 2}{3 - x}$

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

$\frac{(x + 3) (- 1 (- x + 3)) \cdot 2}{3 - x}$

Reorder terms.

$\frac{(x + 3) (- 1 (- x + 3)) \cdot 2}{- x + 3}$

Cancel the common factor.

$\frac{(x + 3) (- 1 (- x + 3)) \cdot 2}{- x + 3}$

Divide $((x + 3) \cdot (- 1)) \cdot 2$ by $1$ .

$((x + 3) \cdot (- 1)) \cdot 2$

Simplify by multiplying through.

Apply the distributive property.

$(x \cdot - 1 + 3 \cdot - 1) \cdot 2$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$(- 1 \cdot x + 3 \cdot - 1) \cdot 2$

Multiply $3$ by $- 1$ .

$(- 1 \cdot x - 3) \cdot 2$

Rewrite $- 1 x$ as $- x$ .

$(- x - 3) \cdot 2$

Simplify by multiplying through.

Apply the distributive property.

$- x \cdot 2 - 3 \cdot 2$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$- 2 x - 6$

Simplify ((x^2-9)/4)/((3-x)/8)

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