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

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

Step 1

Cancel the common factor of $a - b$ and ${(b - a)}^{2}$ .

Factor $- 1$ out of $a$ .

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

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

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

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

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

Reorder terms.

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Factor $- 1$ out of $b$ .

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

Step 5

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

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

Step 6

Simplify the expression.

Rewrite $- (a - b)$ as $- 1 (a - b)$ .

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

Move the negative in front of the fraction.

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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