Divide ((x+2)/(x+8))÷((2x)/3)

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $3$ by $2$ .

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

Step 8

Split the fraction $\frac{3 x + 6}{2 x (x + 8)}$ into two fractions.

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

Step 9

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 10

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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