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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

\frac{1}{y + x}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

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

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

Cross-cancel common factor:

x y

= \frac{1}{y + x}

\frac{5}{2.001 - 2}

∣ x - 1 ∣ > 7

\frac{9}{5} (10) + 32

2 x + 5 < 6

ln (\frac{x}{2})

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