Simplify ((2x)/(x-1))÷((5x)/(2x+4))

$\frac{2 x}{x - 1} \div \frac{5 x}{2 x + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x}{x - 1} \cdot \frac{2 x + 4}{5 x}$

Step 2

Simplify terms.

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2}{x - 1} \cdot \frac{2 x + 4}{5 x}$

Factor $x$ out of $5 x$ .

$\frac{x \cdot 2}{x - 1} \cdot \frac{2 x + 4}{x \cdot 5}$

Cancel the common factor.

$\frac{x \cdot 2}{x - 1} \cdot \frac{2 x + 4}{x \cdot 5}$

Rewrite the expression.

$\frac{2}{x - 1} \cdot \frac{2 x + 4}{5}$

Multiply $\frac{2}{x - 1}$ by $\frac{2 x + 4}{5}$ .

$\frac{2 (2 x + 4)}{(x - 1) \cdot 5}$

Step 3

Simplify the numerator.

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

Factor $2$ out of $2 x$ .

$\frac{2 (2 (x) + 4)}{(x - 1) \cdot 5}$

Factor $2$ out of $4$ .

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

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

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

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

Multiply $2$ by $2$ .

$\frac{4 (x + 2)}{(x - 1) \cdot 5}$

Step 4

Move $5$ to the left of $x - 1$ .

$\frac{4 (x + 2)}{5 (x - 1)}$