Simplify ((x+2)/(x-1))÷(3/(2x))

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

To divide by a fraction, multiply by its reciprocal.

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

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

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

Simplify the expression.

Move $2$ to the left of $x + 2$ .

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

Move $3$ to the left of $x - 1$ .

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

Reorder factors in $\frac{2 (x + 2) x}{3 (x - 1)}$ .

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