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

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

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

simplify

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

\frac{b - a}{b + a}

Solution steps

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

Simplify

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

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

Simplify

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

= \frac{\frac{b - a}{ab}}{\frac{b + a}{ab}}

Apply the fraction rule:

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

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

Cancel

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

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

3 y^{2} + 5 y + 2

3 2^{\frac{1}{2}}

∣ 9 - 2 x ∣ > 11

3 c = c + 32

x^{3} - 216

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