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

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

Step 1

Factor $2$ out of $2 x + 12$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $12$ .

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

Factor $2$ out of $2 x + 2 \cdot 6$ .

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

Step 2

Factor $3$ out of $3 x - 9$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 9$ .

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

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

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

Step 3

Factor $2$ out of $6 - 2 x$ .

Factor $2$ out of $6$ .

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

Factor $2$ out of $- 2 x$ .

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

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

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

Step 4

Multiply $\frac{2 (x + 6)}{3 (x - 3)} \cdot \frac{2 (3 - x)}{3 x + 8}$ .

Multiply $\frac{2 (x + 6)}{3 (x - 3)}$ by $\frac{2 (3 - x)}{3 x + 8}$ .

$\frac{2 (x + 6) (2 (3 - x))}{3 (x - 3) (3 x + 8)}$

Multiply $2$ by $2$ .

$\frac{4 (x + 6) (3 - x)}{3 (x - 3) (3 x + 8)}$

Step 5

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

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

$\frac{4 (x + 6) (- 1 (- 3) - x)}{3 (x - 3) (3 x + 8)}$

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

$\frac{4 (x + 6) (- 1 (- 3) - (x))}{3 (x - 3) (3 x + 8)}$

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

$\frac{4 (x + 6) (- 1 (- 3 + x))}{3 (x - 3) (3 x + 8)}$

Reorder terms.

$\frac{4 (x + 6) (- 1 (x - 3))}{3 (x - 3) (3 x + 8)}$

Cancel the common factor.

$\frac{4 (x + 6) (- 1 (x - 3))}{3 (x - 3) (3 x + 8)}$

Rewrite the expression.

$\frac{4 (x + 6) \cdot (- 1)}{3 (3 x + 8)}$

Step 6

Simplify the expression.

Multiply $- 1$ by $4$ .

$\frac{- 4 (x + 6)}{3 (3 x + 8)}$

Move the negative in front of the fraction.

$- \frac{4 (x + 6)}{3 (3 x + 8)}$

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

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