Simplify 1/(y^2)-1/x

$\frac{1}{y^{2}} - \frac{1}{x}$

To write $\frac{1}{y^{2}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{y^{2}} \cdot \frac{x}{x} - \frac{1}{x}$

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

$\frac{1}{y^{2}} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{y^{2}}{y^{2}}$

Write each expression with a common denominator of $x y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{y^{2}}$ by $\frac{x}{x}$ .

$\frac{x}{y^{2} x} - \frac{1}{x} \cdot \frac{y^{2}}{y^{2}}$

Multiply $\frac{1}{x}$ by $\frac{y^{2}}{y^{2}}$ .

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

Reorder the factors of $x y^{2}$ .

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

Combine the numerators over the common denominator.

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