Simplify (1/(3(x+2)))÷((5x)/(6(x+2)))

$\frac{1}{3 (x + 2)} \div \frac{5 x}{6 (x + 2)}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{3 (x + 2)} \cdot \frac{6 (x + 2)}{5 x}$

Step 2

Cancel the common factor of $3 (x + 2)$ .

Factor $3 (x + 2)$ out of $6 (x + 2)$ .

$\frac{1}{3 (x + 2)} \cdot \frac{3 (x + 2) (2)}{5 x}$

Cancel the common factor.

$\frac{1}{3 (x + 2)} \cdot \frac{3 (x + 2) \cdot 2}{5 x}$

Rewrite the expression.

$\frac{2}{5 x}$