Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Cancel the common factor of $a - b$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

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

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Step 4.1

Factor $- 1$ out of $b$ .

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

Step 4.2

Factor $- 1$ out of $- a$ .

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

Step 4.3

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

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

Step 4.4

Reorder terms.

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

Step 4.5

Cancel the common factor.

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

Step 4.6

Rewrite the expression.

$\frac{- 1}{b}$

Step 5

Move the negative in front of the fraction.

$- \frac{1}{b}$