What is (2a^{-1}+3b^{-2})/(a^{-1)-b^{-1}} ?

The solution to (2a^{-1}+3b^{-2})/(a^{-1)-b^{-1}} is (2b^2+3a)/(b(b-a))

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simplify (2a^{-1}+3b^{-2})/(a^{-1)-b^{-1}}

simplify

\frac{2 a ^{- 1} + 3 b ^{- 2}}{a ^{- 1} - b ^{- 1}}

\frac{2 b ^{2} + 3 a}{b ( b - a )}

Solution steps

\frac{2 a ^{- 1} + 3 b ^{- 2}}{a ^{- 1} - b ^{- 1}}

Simplify

2 a^{- 1} + 3 b^{- 2} : \frac{2 b ^{2} + 3 a}{a b ^{2}}

= \frac{\frac{2 b ^{2} + 3 a}{a b ^{2}}}{a ^{- 1} - b ^{- 1}}

Simplify

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

= \frac{\frac{2 b ^{2} + 3 a}{a b ^{2}}}{\frac{b - a}{ab}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 2 b ^{2} + 3 a ) ab}{a b ^{2} ( b - a )}

Cancel

\frac{( 2 b ^{2} + 3 a ) ab}{a b ^{2} ( b - a )} : \frac{2 b ^{2} + 3 a}{b ( b - a )}

= \frac{2 b ^{2} + 3 a}{b ( b - a )}

36.25

5112

\frac{3}{x ^{2} - 3 x} - \frac{4}{x ^{2} - 4 x + 3}

(2 x - 2) (2 x + 2)

14 + 3 y^{2} + 30 y - 3 y^{2} - 4 y - 14 - 16 y

What is (2a^{-1}+3b^{-2})/(a^{-1)-b^{-1}} ?
The solution to (2a^{-1}+3b^{-2})/(a^{-1)-b^{-1}} is (2b^2+3a)/(b(b-a))