Simplify ((x+2)/(x+8))÷((2x)/3)

$\frac{x + 2}{x + 8} \div \frac{2 x}{3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 2}{x + 8} \cdot \frac{3}{2 x}$

Multiply $\frac{x + 2}{x + 8}$ by $\frac{3}{2 x}$ .

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

Simplify the expression.

Move $3$ to the left of $x + 2$ .

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

Move $2$ to the left of $x + 8$ .

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

Reorder factors in $\frac{3 (x + 2)}{2 (x + 8) x}$ .

$\frac{3 (x + 2)}{2 x (x + 8)}$