Simplify 5/(2x)+4/(3y)

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

Step 1

To write $\frac{5}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

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

Step 2

To write $\frac{4}{3 y}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

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

Step 3

Write each expression with a common denominator of $6 x y$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

$\frac{5 (3 y)}{6 x y} + \frac{4}{3 y} \cdot \frac{2 x}{2 x}$

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

$\frac{5 (3 y)}{6 x y} + \frac{4 (2 x)}{3 y (2 x)}$

Multiply $2$ by $3$ .

$\frac{5 (3 y)}{6 x y} + \frac{4 (2 x)}{6 y x}$

Reorder the factors of $6 y x$ .

$\frac{5 (3 y)}{6 x y} + \frac{4 (2 x)}{6 x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (3 y) + 4 (2 x)}{6 x y}$

Step 5

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 y + 4 \cdot 2 x}{6 x y}$

Multiply $4$ by $2$ .

$\frac{15 y + 8 x}{6 x y}$