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

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

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

simplify

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

- \frac{x}{x + 1}

Solution steps

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

Factor

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

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

Factor

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

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

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

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

Cancel the common factor:

x - 1

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

Apply the fraction rule:

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

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

6 (5)

5 b x 3 n

1 \frac{1}{7}

x^{2} - 6 x - 5 x^{2} - 7 x - 10

(- x - 6)^{2}