What is a/(ab-b^2)-1/b ?

The solution to a/(ab-b^2)-1/b is -1/(b-a)

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

simplify

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

- \frac{1}{b - a}

Solution steps

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

Least Common Multiplier of

ab - b^{2}, b : b (- b^{2} + ab)

Adjust Fractions based on the LCM

= \frac{ab}{b ( - b ^{2} + ab )} - \frac{- b ^{2} + ab}{b ( - b ^{2} + ab )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{ab - ( - b ^{2} + ab )}{b ( - b ^{2} + ab )}

Simplify

ab - (- b^{2} + ab) : b^{2}

= \frac{b ^{2}}{b ( - b ^{2} + ab )}

Cancel

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

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

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