Simplify 3/x+5/y

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

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

Reorder the factors of $y x$ .

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

Step 4

Combine the numerators over the common denominator.

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