What is (x-x^2)/(2-3x+x^2) ?

The solution to (x-x^2)/(2-3x+x^2) is -x/(x-2)

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simplify (x-x^2)/(2-3x+x^2)

simplify

\frac{x - x ^{2}}{2 - 3 x + x ^{2}}

- \frac{x}{x - 2}

Solution steps

\frac{x - x ^{2}}{2 - 3 x + x ^{2}}

Factor

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

= \frac{x ( 1 - x )}{2 - 3 x + x ^{2}}

Factor

2 - 3 x + 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{7 x ^{2}}{x ^{3}}

25 x^{7} y^{2}

\frac{2}{5} (150)

\frac{5}{4} \div \frac{1}{4}

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