Simplify ((4x)/(5+x))/((6x)/(x+2))

$\frac{\frac{4 x}{5 + x}}{\frac{6 x}{x + 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 x}{5 + x} \cdot \frac{x + 2}{6 x}$

Step 2

Cancel the common factor of $2 x$ .

Factor $2 x$ out of $4 x$ .

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

Factor $2 x$ out of $6 x$ .

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

Cancel the common factor.

$\frac{2 x \cdot 2}{5 + x} \cdot \frac{x + 2}{2 x \cdot 3}$

Rewrite the expression.

$\frac{2}{5 + x} \cdot \frac{x + 2}{3}$

Step 3

Multiply $\frac{2}{5 + x}$ by $\frac{x + 2}{3}$ .

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

Step 4

Move $3$ to the left of $5 + x$ .

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