What is (x^{-1}+y^{-1})^{-2} ?

The solution to (x^{-1}+y^{-1})^{-2} is (x^2y^2)/((y+x)^2)

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})^{-2}

simplify

(x^{- 1} + y^{- 1})^{- 2}

\frac{x ^{2} y ^{2}}{( y + x ) ^{2}}

Solution steps

(x^{- 1} + y^{- 1})^{- 2}

Apply exponent rule:

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

(x^{- 1} + y^{- 1})^{- 2} = \frac{1}{( x ^{- 1} + y ^{- 1} ) ^{2}}

= \frac{1}{( x ^{- 1} + y ^{- 1} ) ^{2}}

Simplify

(x^{- 1} + y^{- 1})^{2} : \frac{( y + x ) ^{2}}{x ^{2} y ^{2}}

= \frac{1}{\frac{( y + x ) ^{2}}{x ^{2} y ^{2}}}

Apply the fraction rule:

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

= \frac{x ^{2} y ^{2}}{( y + x ) ^{2}}

(5)^{- 1}

\frac{3}{4} (x + 3) = 9

∣ - 9 x ∣ = 64

(\frac{4 x ^{2} y}{x ^{- 5}})^{- 3}

What is (x^{-1}+y^{-1})^{-2} ?
The solution to (x^{-1}+y^{-1})^{-2} is (x^2y^2)/((y+x)^2)