Simplify ((5x+2)/(3xy^2))÷((10x+4)/(x^2y))

$\frac{5 x + 2}{3 x y^{2}} \div \frac{10 x + 4}{x^{2} y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x + 2}{3 x y^{2}} \cdot \frac{x^{2} y}{10 x + 4}$

Step 2

Simplify terms.

Cancel the common factor of $x y$ .

Factor $x y$ out of $3 x y^{2}$ .

$\frac{5 x + 2}{x y (3 y)} \cdot \frac{x^{2} y}{10 x + 4}$

Factor $x y$ out of $x^{2} y$ .

$\frac{5 x + 2}{x y (3 y)} \cdot \frac{x y (x)}{10 x + 4}$

Cancel the common factor.

$\frac{5 x + 2}{x y (3 y)} \cdot \frac{x y x}{10 x + 4}$

Rewrite the expression.

$\frac{5 x + 2}{3 y} \cdot \frac{x}{10 x + 4}$

Multiply $\frac{5 x + 2}{3 y}$ by $\frac{x}{10 x + 4}$ .

$\frac{(5 x + 2) x}{3 y (10 x + 4)}$

Step 3

Simplify the denominator.

Factor $2$ out of $10 x + 4$ .

Factor $2$ out of $10 x$ .

$\frac{(5 x + 2) x}{3 y (2 (5 x) + 4)}$

Factor $2$ out of $4$ .

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

Factor $2$ out of $2 (5 x) + 2 (2)$ .

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

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

Multiply $2$ by $3$ .

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

Step 4

Cancel the common factor of $5 x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{6 y}$