What is (a^{-2}+b^{-1})/(a^{-1)-5b^{-3}} ?

The solution to (a^{-2}+b^{-1})/(a^{-1)-5b^{-3}} is ((b+a^2)b^2)/(a(b^3-5a))

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simplify (a^{-2}+b^{-1})/(a^{-1)-5b^{-3}}

simplify

\frac{a ^{- 2} + b ^{- 1}}{a ^{- 1} - 5 b ^{- 3}}

\frac{( b + a ^{2} ) b ^{2}}{a ( b ^{3} - 5 a )}

Solution steps

\frac{a ^{- 2} + b ^{- 1}}{a ^{- 1} - 5 b ^{- 3}}

Simplify

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

= \frac{\frac{b + a ^{2}}{a ^{2} b}}{a ^{- 1} - 5 b ^{- 3}}

Simplify

a^{- 1} - 5 b^{- 3} : \frac{b ^{3} - 5 a}{a b ^{3}}

= \frac{\frac{b + a ^{2}}{a ^{2} b}}{\frac{b ^{3} - 5 a}{a b ^{3}}}

Apply the fraction rule:

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

= \frac{( b + a ^{2} ) a b ^{3}}{a ^{2} b ( b ^{3} - 5 a )}

Cancel

\frac{( b + a ^{2} ) a b ^{3}}{a ^{2} b ( b ^{3} - 5 a )} : \frac{( b + a ^{2} ) b ^{2}}{a ( b ^{3} - 5 a )}

= \frac{( b + a ^{2} ) b ^{2}}{a ( b ^{3} - 5 a )}

x^{2} + y^{2}

\frac{\frac{1}{a} - \frac{9}{a ^{2}} + \frac{20}{a ^{3}}}{\frac{16}{a} - a}

(- 8 x)^{- 2}

8 3^{2}

What is (a^{-2}+b^{-1})/(a^{-1)-5b^{-3}} ?
The solution to (a^{-2}+b^{-1})/(a^{-1)-5b^{-3}} is ((b+a^2)b^2)/(a(b^3-5a))