Simplify 1/(x^2)-1/(x^3)

$\frac{1}{x^{2}} - \frac{1}{x^{3}}$

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

$\frac{1}{x^{2}} \cdot \frac{x}{x} - \frac{1}{x^{3}}$

Write each expression with a common denominator of $x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x}{x^{2} x} - \frac{1}{x^{3}}$

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

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

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

$\frac{x}{x^{2} x^{1}} - \frac{1}{x^{3}}$

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

$\frac{x}{x^{2 + 1}} - \frac{1}{x^{3}}$

Add $2$ and $1$ .

$\frac{x}{x^{3}} - \frac{1}{x^{3}}$

Combine the numerators over the common denominator.

$\frac{x - 1}{x^{3}}$