Simplify a/(a-b)+b/(b-a)

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

Factor $- 1$ out of $b$ .

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

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

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

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

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

Simplify the expression.

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Move a negative from the denominator of $\frac{b}{- 1 (- b + a)}$ to the numerator.

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

Reorder terms.

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

Combine the numerators over the common denominator.

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

Cancel the common factor of $a - b$ .

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Cancel the common factor.

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

Divide $1$ by $1$ .

$1$

Simplify a/(a-b)+b/(b-a)

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