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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((1+x^{-1}))/(1-x^{-2)}

simplify

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

\frac{x}{x - 1}

Solution steps

\frac{1 + x ^{- 1}}{1 - x ^{- 2}}

Apply exponent rule:

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

x^{- 2} = \frac{1}{x ^{2}}

= \frac{1 + x ^{- 1}}{1 - \frac{1}{x ^{2}}}

Apply exponent rule:

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

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

= \frac{1 + \frac{1}{x}}{1 - \frac{1}{x ^{2}}}

Join

1 - \frac{1}{x ^{2}} : \frac{x ^{2} - 1}{x ^{2}}

= \frac{1 + \frac{1}{x}}{\frac{x ^{2} - 1}{x ^{2}}}

Join

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

= \frac{\frac{x + 1}{x}}{\frac{x ^{2} - 1}{x ^{2}}}

Divide fractions:

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

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

Cancel the common factor:

x

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

Factor

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

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

Cancel the common factor:

x + 1

= \frac{x}{x - 1}

8 (3 x + 4) - 20

(10 x - x^{2} + 8) + (5 x^{2} + 1 - 22 x)

- x \cdot (- y)

(\frac{d ^{2}}{3} + z^{3})^{3}

3 \frac{7}{10}

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