Simplify 1/(b^2-ab)-1/(ab-a^2)

$\frac{1}{b^{2} - a b} - \frac{1}{a b - a^{2}}$

Simplify each term.

Factor $b$ out of $b^{2} - a b$ .

Factor $b$ out of $b^{2}$ .

$\frac{1}{b \cdot b - a b} - \frac{1}{a b - a^{2}}$

Factor $b$ out of $- a b$ .

$\frac{1}{b \cdot b + b (- a)} - \frac{1}{a b - a^{2}}$

Factor $b$ out of $b \cdot b + b (- a)$ .

$\frac{1}{b (b - a)} - \frac{1}{a b - a^{2}}$

Factor $a$ out of $a b - a^{2}$ .

Factor $a$ out of $a b$ .

$\frac{1}{b (b - a)} - \frac{1}{a (b) - a^{2}}$

Factor $a$ out of $- a^{2}$ .

$\frac{1}{b (b - a)} - \frac{1}{a (b) + a (- a)}$

Factor $a$ out of $a (b) + a (- a)$ .

$\frac{1}{b (b - a)} - \frac{1}{a (b - a)}$

To write $\frac{1}{b (b - a)}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{1}{b (b - a)} \cdot \frac{a}{a} - \frac{1}{a (b - a)}$

To write $- \frac{1}{a (b - a)}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{1}{b (b - a)} \cdot \frac{a}{a} - \frac{1}{a (b - a)} \cdot \frac{b}{b}$

Write each expression with a common denominator of $b (b - a) a$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{b (b - a)}$ by $\frac{a}{a}$ .

$\frac{a}{b (b - a) a} - \frac{1}{a (b - a)} \cdot \frac{b}{b}$

Multiply $\frac{1}{a (b - a)}$ by $\frac{b}{b}$ .

$\frac{a}{b (b - a) a} - \frac{b}{a (b - a) b}$

Reorder the factors of $b (b - a) a$ .

$\frac{a}{a b (b - a)} - \frac{b}{a (b - a) b}$

Reorder the factors of $a (b - a) b$ .

$\frac{a}{a b (b - a)} - \frac{b}{a b (b - a)}$

Combine the numerators over the common denominator.

$\frac{a - b}{a b (b - a)}$

Cancel the common factor of $a - b$ and $b - a$ .

Factor $- 1$ out of $a$ .

$\frac{- 1 (- a) - b}{a b (b - a)}$

Factor $- 1$ out of $- b$ .

$\frac{- 1 (- a) - (b)}{a b (b - a)}$

Factor $- 1$ out of $- 1 (- a) - (b)$ .

$\frac{- 1 (- a + b)}{a b (b - a)}$

Reorder terms.

$\frac{- 1 (- a + b)}{a b (- a + b)}$

Cancel the common factor.

$\frac{- 1 (- a + b)}{a b (- a + b)}$

Rewrite the expression.

$\frac{- 1}{a b}$

Move the negative in front of the fraction.

$- \frac{1}{a b}$

Simplify 1/(b^2-ab)-1/(ab-a^2)

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