Simplify ((8x+48)/(x^2-3x-54))÷((x-3)/(x^2-6x-27))

$\frac{8 x + 48}{x^{2} - 3 x - 54} \div \frac{x - 3}{x^{2} - 6 x - 27}$

To divide by a fraction, multiply by its reciprocal.

$\frac{8 x + 48}{x^{2} - 3 x - 54} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Factor $8$ out of $8 x + 48$ .

Factor $8$ out of $8 x$ .

$\frac{8 (x) + 48}{x^{2} - 3 x - 54} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Factor $8$ out of $48$ .

$\frac{8 x + 8 \cdot 6}{x^{2} - 3 x - 54} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Factor $8$ out of $8 x + 8 \cdot 6$ .

$\frac{8 (x + 6)}{x^{2} - 3 x - 54} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Factor $x^{2} - 3 x - 54$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 54$ and whose sum is $- 3$ .

$- 9, 6$

Write the factored form using these integers.

$\frac{8 (x + 6)}{(x - 9) (x + 6)} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{8 (x + 6)}{(x - 9) (x + 6)} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Rewrite the expression.

$\frac{8}{x - 9} \cdot \frac{x^{2} - 6 x - 27}{x - 3}$

Factor $x^{2} - 6 x - 27$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 27$ and whose sum is $- 6$ .

$- 9, 3$

Write the factored form using these integers.

$\frac{8}{x - 9} \cdot \frac{(x - 9) (x + 3)}{x - 3}$

Simplify terms.

Cancel the common factor of $x - 9$ .

Cancel the common factor.

$\frac{8}{x - 9} \cdot \frac{(x - 9) (x + 3)}{x - 3}$

Rewrite the expression.

$8 \frac{x + 3}{x - 3}$

Combine $8$ and $\frac{x + 3}{x - 3}$ .

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

Simplify ((8x+48)/(x^2-3x-54))÷((x-3)/(x^2-6x-27))

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