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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Simplify

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

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

Cancel

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

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

2 \times (- 0.05) \times 0.3

\frac{6}{12}

∣ x ∣ ∣ x ∣

\frac{1}{3} \times 0

5 x + 45

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