What is (3^{-1}-5^{-1})^{-1} ?

The solution to (3^{-1}-5^{-1})^{-1} is 15/2

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simplify (3^{-1}-5^{-1})^{-1}

simplify

(3^{- 1} - 5^{- 1})^{- 1}

\frac{15}{2}

Decimal Notation

7.5

Solution steps

(3^{- 1} - 5^{- 1})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(3^{- 1} - 5^{- 1})^{- 1} = \frac{1}{3 ^{- 1} - 5 ^{- 1}}

= \frac{1}{3 ^{- 1} - 5 ^{- 1}}

Simplify

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

= \frac{1}{\frac{1}{3} - \frac{1}{5}}

Join

\frac{1}{3} - \frac{1}{5} : \frac{2}{15}

= \frac{1}{\frac{2}{15}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{15}{2}

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x - (- x)

\frac{sin ( x )}{1 + sin ( x )}