Simplify (9x+18)/(x^2-2x-8)*(3x-12)/(6x)

$\frac{9 x + 18}{x^{2} - 2 x - 8} \cdot \frac{3 x - 12}{6 x}$

Step 1

Factor $9$ out of $9 x + 18$ .

Factor $9$ out of $9 x$ .

$\frac{9 (x) + 18}{x^{2} - 2 x - 8} \cdot \frac{3 x - 12}{6 x}$

Factor $9$ out of $18$ .

$\frac{9 x + 9 \cdot 2}{x^{2} - 2 x - 8} \cdot \frac{3 x - 12}{6 x}$

Factor $9$ out of $9 x + 9 \cdot 2$ .

$\frac{9 (x + 2)}{x^{2} - 2 x - 8} \cdot \frac{3 x - 12}{6 x}$

Step 2

Factor $x^{2} - 2 x - 8$ 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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Write the factored form using these integers.

$\frac{9 (x + 2)}{(x - 4) (x + 2)} \cdot \frac{3 x - 12}{6 x}$

Step 3

Simplify terms.

Factor $3$ out of $3 x - 12$ .

Factor $3$ out of $3 x$ .

$\frac{9 (x + 2)}{(x - 4) (x + 2)} \cdot \frac{3 (x) - 12}{6 x}$

Factor $3$ out of $- 12$ .

$\frac{9 (x + 2)}{(x - 4) (x + 2)} \cdot \frac{3 x + 3 \cdot - 4}{6 x}$

Factor $3$ out of $3 x + 3 \cdot - 4$ .

$\frac{9 (x + 2)}{(x - 4) (x + 2)} \cdot \frac{3 (x - 4)}{6 x}$

Cancel the common factor of $3$ .

Factor $3$ out of $9 (x + 2)$ .

$\frac{3 (3 (x + 2))}{(x - 4) (x + 2)} \cdot \frac{3 (x - 4)}{6 x}$

Factor $3$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 4$ .

Factor $x - 4$ out of $3 (x - 4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{3 (x + 2)}{x + 2}$ by $\frac{3}{2 x}$ .

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

Multiply $3$ by $3$ .

$\frac{9 (x + 2)}{(x + 2) (2 x)}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{9 (x + 2)}{(x + 2) (2 x)}$

Rewrite the expression.

$\frac{9}{2 x}$

Simplify (9x+18)/(x^2-2x-8)*(3x-12)/(6x)

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