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

The solution to (x^{-1}-x^{-2})/(x-x^2) is -1/(x^3)

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

simplify

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

- \frac{1}{x ^{3}}

Solution steps

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

Simplify

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

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

Join

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

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

Apply the fraction rule:

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

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

Factor

x^{2} (x - x^{2}) : x^{3} (1 - x)

= \frac{x - 1}{x ^{3} ( 1 - x )}

Cancel

\frac{x - 1}{x ^{3} ( 1 - x )} : - \frac{1}{x ^{3}}

= - \frac{1}{x ^{3}}

i^{130}

(32 - 46)^{2}

a (x - 1) - (a + 3) (x - 1)

\frac{3}{10} \div 4

(2 + i 3)^{3}

What is (x^{-1}-x^{-2})/(x-x^2) ?
The solution to (x^{-1}-x^{-2})/(x-x^2) is -1/(x^3)