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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Simplify

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

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

Cancel

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

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

- 6 q + 1 \geq 2 q - 10

3 m^{2} \leq 9 m

12 - 5 (x + 3) = 2 x - 5

25 x^{4} 20 x^{2} y + 4 y^{2}

x 2 = 9

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