Simplify 3/(3xy)+(2y)/(6x)

$\frac{3}{3 x y} + \frac{2 y}{6 x}$

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{3 x y} + \frac{2 y}{6 x}$

Rewrite the expression.

$\frac{1}{x y} + \frac{2 y}{6 x}$

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

Factor $2$ out of $2 y$ .

$\frac{1}{x y} + \frac{2 (y)}{6 x}$

Cancel the common factors.

Factor $2$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x y} + \frac{y}{3 x}$

To write $\frac{1}{x y}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{x y} \cdot \frac{3}{3} + \frac{y}{3 x}$

To write $\frac{y}{3 x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{1}{x y} \cdot \frac{3}{3} + \frac{y}{3 x} \cdot \frac{y}{y}$

Write each expression with a common denominator of $x y \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x y}$ by $\frac{3}{3}$ .

$\frac{3}{x y \cdot 3} + \frac{y}{3 x} \cdot \frac{y}{y}$

Multiply $\frac{y}{3 x}$ by $\frac{y}{y}$ .

$\frac{3}{x y \cdot 3} + \frac{y \cdot y}{3 x y}$

Reorder the factors of $x y \cdot 3$ .

$\frac{3}{3 x y} + \frac{y \cdot y}{3 x y}$

Combine the numerators over the common denominator.

$\frac{3 + y \cdot y}{3 x y}$

Multiply $y$ by $y$ .

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