Simplify (5x+10)/(4x-8)*(4-2x)/(x+2)

$\frac{5 x + 10}{4 x - 8} \cdot \frac{4 - 2 x}{x + 2}$

Simplify terms.

Factor $5$ out of $5 x + 10$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 10}{4 x - 8} \cdot \frac{4 - 2 x}{x + 2}$

Factor $5$ out of $10$ .

$\frac{5 x + 5 \cdot 2}{4 x - 8} \cdot \frac{4 - 2 x}{x + 2}$

Factor $5$ out of $5 x + 5 \cdot 2$ .

$\frac{5 (x + 2)}{4 x - 8} \cdot \frac{4 - 2 x}{x + 2}$

Factor $4$ out of $4 x - 8$ .

Factor $4$ out of $4 x$ .

$\frac{5 (x + 2)}{4 (x) - 8} \cdot \frac{4 - 2 x}{x + 2}$

Factor $4$ out of $- 8$ .

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

Factor $4$ out of $4 x + 4 \cdot - 2$ .

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

Factor $2$ out of $4 - 2 x$ .

Factor $2$ out of $4$ .

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

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

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

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

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

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $5 (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4 (x - 2)$ .

$\frac{5}{2 (2 (x - 2))} \cdot (2 (2 - x))$

Cancel the common factor.

$\frac{5}{2 (2 (x - 2))} \cdot (2 (2 - x))$

Rewrite the expression.

$\frac{5}{2 (x - 2)} \cdot (2 - x)$

Multiply $\frac{5}{2 (x - 2)}$ by $2 - x$ .

$\frac{5 (2 - x)}{2 (x - 2)}$

Cancel the common factor of $2 - x$ and $x - 2$ .

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{5 (- 1 (- 2) - x)}{2 (x - 2)}$

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

$\frac{5 (- 1 (- 2) - (x))}{2 (x - 2)}$

Factor $- 1$ out of $- 1 (- 2) - (x)$ .

$\frac{5 (- 1 (- 2 + x))}{2 (x - 2)}$

Reorder terms.

$\frac{5 (- 1 (x - 2))}{2 (x - 2)}$

Cancel the common factor.

$\frac{5 (- 1 (x - 2))}{2 (x - 2)}$

Rewrite the expression.

$\frac{5 \cdot (- 1)}{2}$

Multiply $5$ by $- 1$ .

$\frac{- 5}{2}$

Move the negative in front of the fraction.

$- \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{2}$

Decimal Form:

$- 2.5$

Mixed Number Form:

$- 2 \frac{1}{2}$

Simplify (5x+10)/(4x-8)*(4-2x)/(x+2)

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