Simplify 2/3+(3x+4y)/(3y)

$\frac{2}{3} + \frac{3 x + 4 y}{3 y}$

Step 1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

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

Step 2

Simplify terms.

Multiply $\frac{2}{3}$ by $\frac{y}{y}$ .

$\frac{2 y}{3 y} + \frac{3 x + 4 y}{3 y}$

Combine the numerators over the common denominator.

$\frac{2 y + 3 x + 4 y}{3 y}$

Step 3

Simplify the numerator.

Add $2 y$ and $4 y$ .

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

Factor $3$ out of $3 x + 6 y$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6 y}{3 y}$

Factor $3$ out of $6 y$ .

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

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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