Simplify x/y-y/z

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $\frac{y}{z}$ by $\frac{y}{y}$ .

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

Reorder the factors of $z y$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{x z - (y \cdot y)}{y z}$

Multiply $y$ by $y$ .

$\frac{x z - y^{2}}{y z}$