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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

Apply the fraction rule:

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

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

\frac{7}{20} + \frac{7}{12}

2 (3 (3 (x^{2} + 2) - 2 (x^{2} - 5)))

2 (2 + 1)^{0}

8 x y (x + 8 y)

\frac{1 + cos ( 2 x )}{cot ( x )}

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