Simplify (ax+ay)/(xy^2)*(x^2y)/(3x+3y)

$\frac{a x + a y}{x y^{2}} \cdot \frac{x^{2} y}{3 x + 3 y}$

Factor $a$ out of $a x + a y$ .

Factor $a$ out of $a x$ .

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

Factor $a$ out of $a y$ .

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

Factor $a$ out of $a (x) + a (y)$ .

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

Factor $3$ out of $3 x + 3 y$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3 y$ .

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

Factor $3$ out of $3 (x) + 3 (y)$ .

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

Combine.

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

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a (x^{2} y)}{x y^{2} \cdot (3)}$

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $a (x^{2} y)$ .

$\frac{x (a (x y))}{x y^{2} \cdot (3)}$

Cancel the common factors.

Factor $x$ out of $x y^{2} \cdot (3)$ .

$\frac{x (a (x y))}{x (y^{2} \cdot (3))}$

Cancel the common factor.

$\frac{x (a (x y))}{x (y^{2} \cdot (3))}$

Rewrite the expression.

$\frac{a (x y)}{y^{2} \cdot (3)}$

Cancel the common factor of $y$ and $y^{2}$ .

Factor $y$ out of $a (x y)$ .

$\frac{y (a (x))}{y^{2} \cdot (3)}$

Cancel the common factors.

Factor $y$ out of $y^{2} \cdot (3)$ .

$\frac{y (a (x))}{y (y \cdot 3)}$

Cancel the common factor.

$\frac{y (a (x))}{y (y \cdot 3)}$

Rewrite the expression.

$\frac{a (x)}{y \cdot 3}$

Move $3$ to the left of $y$ .

$\frac{a x}{3 y}$