What is (x^{-1}+y^{-1})^{-1} ?

The solution to (x^{-1}+y^{-1})^{-1} is (xy)/(y+x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x^{-1}+y^{-1})^{-1}

simplify

(x^{- 1} + y^{- 1})^{- 1}

\frac{x y}{y + x}

Solution steps

(x^{- 1} + y^{- 1})^{- 1}

Apply exponent rule:

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

(x^{- 1} + y^{- 1})^{- 1} = \frac{1}{x ^{- 1} + y ^{- 1}}

= \frac{1}{x ^{- 1} + y ^{- 1}}

Simplify

x^{- 1} + y^{- 1} : \frac{1}{x} + \frac{1}{y}

= \frac{1}{\frac{1}{x} + \frac{1}{y}}

Join

\frac{1}{x} + \frac{1}{y} : \frac{y + x}{x y}

= \frac{1}{\frac{y + x}{x y}}

Apply the fraction rule:

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

= \frac{x y}{y + x}

1 8^{2} = 12 (12 + x)

ln (0.99)

- \frac{186}{200} + 0.3

x^{2} + 3 x - 108

2 n^{2} + 16 n + 14

What is (x^{-1}+y^{-1})^{-1} ?
The solution to (x^{-1}+y^{-1})^{-1} is (xy)/(y+x)