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

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

simplify

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

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

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

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

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

Cancel

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

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

\frac{90}{180}

(\frac{2}{3 ^{2}})^{- 2} \cdot (\frac{2 ^{2}}{3 ^{3}})

(- 5 d + 8) (d - 3)

- \frac{3}{9}

0 \times x

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