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

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

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simplify (x-x^2)/(x^2+x-2)

simplify

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

- \frac{x}{x + 2}

Solution steps

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

Factor

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

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

Factor

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

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

x (1 - x) = - x (x - 1)

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

Cancel the common factor:

x - 1

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

Apply the fraction rule:

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

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

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

- 3 \div \frac{1}{3}

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

3 x^{3} + 27 x^{2} + 60 x

6 x^{2} y^{2} - 8 x y^{5}