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

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

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Multiply $y$ by $y^{2}$ by adding the exponents.

Multiply $y$ by $y^{2}$ .

Raise $y$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$\frac{y^{3} - x}{y^{2} x}$