Evaluate 1/x-1/y

$\frac{1}{x} - \frac{1}{y}$

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

$\frac{1}{x} \cdot \frac{y}{y} - \frac{1}{y}$

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

$\frac{1}{x} \cdot \frac{y}{y} - \frac{1}{y} \cdot \frac{x}{x}$

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

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

$\frac{y}{x y} - \frac{1}{y} \cdot \frac{x}{x}$

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

$\frac{y}{x y} - \frac{x}{y x}$

Reorder the factors of $y x$ .

$\frac{y}{x y} - \frac{x}{x y}$

Combine the numerators over the common denominator.

$\frac{y - x}{x y}$