Divide ((2x)/(4x+3))÷((x-1)/(2x))

$\frac{2 x}{4 x + 3} \div \frac{x - 1}{2 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x}{4 x + 3} \cdot \frac{2 x}{x - 1}$

Step 2

Multiply $\frac{2 x}{4 x + 3} \cdot \frac{2 x}{x - 1}$ .

Multiply $\frac{2 x}{4 x + 3}$ by $\frac{2 x}{x - 1}$ .

$\frac{2 x (2 x)}{(4 x + 3) (x - 1)}$

Multiply $2$ by $2$ .

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

Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

$\frac{4 x^{2}}{(4 x + 3) (x - 1)}$