Simplify ((5x-10)/(2x))÷((3x-6)/(2x+8))

$\frac{5 x - 10}{2 x} \div \frac{3 x - 6}{2 x + 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x - 10}{2 x} \cdot \frac{2 x + 8}{3 x - 6}$

Step 2

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

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 10}{2 x} \cdot \frac{2 x + 8}{3 x - 6}$

Factor $5$ out of $- 10$ .

$\frac{5 x + 5 \cdot - 2}{2 x} \cdot \frac{2 x + 8}{3 x - 6}$

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

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 x + 8}{3 x - 6}$

Step 3

Factor $2$ out of $2 x + 8$ .

Factor $2$ out of $2 x$ .

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 (x) + 8}{3 x - 6}$

Factor $2$ out of $8$ .

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 x + 2 \cdot 4}{3 x - 6}$

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

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 (x + 4)}{3 x - 6}$

Step 4

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 (x + 4)}{3 (x) - 6}$

Factor $3$ out of $- 6$ .

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 (x + 4)}{3 x + 3 \cdot - 2}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{5 (x - 2)}{2 x} \cdot \frac{2 (x + 4)}{3 (x - 2)}$

Step 5

Cancel the common factor of $x - 2$ .

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

$\frac{(x - 2) \cdot 5}{2 x} \cdot \frac{2 (x + 4)}{3 (x - 2)}$

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

$\frac{(x - 2) \cdot 5}{2 x} \cdot \frac{2 (x + 4)}{(x - 2) \cdot 3}$

Cancel the common factor.

$\frac{(x - 2) \cdot 5}{2 x} \cdot \frac{2 (x + 4)}{(x - 2) \cdot 3}$

Rewrite the expression.

$\frac{5}{2 x} \cdot \frac{2 (x + 4)}{3}$

Step 6

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{5}{2 (x)} \cdot \frac{2 (x + 4)}{3}$

Cancel the common factor.

$\frac{5}{2 x} \cdot \frac{2 (x + 4)}{3}$

Rewrite the expression.

$\frac{5}{x} \cdot \frac{x + 4}{3}$

Step 7

Multiply $\frac{5}{x}$ by $\frac{x + 4}{3}$ .

$\frac{5 (x + 4)}{x \cdot 3}$

Step 8

Move $3$ to the left of $x$ .

$\frac{5 (x + 4)}{3 x}$

Simplify ((5x-10)/(2x))÷((3x-6)/(2x+8))

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