What is (4-3x-x^2)/(x^2-1) ?

The solution to (4-3x-x^2)/(x^2-1) is -(x+4)/(x+1)

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simplify (4-3x-x^2)/(x^2-1)

simplify

\frac{4 - 3 x - x ^{2}}{x ^{2} - 1}

- \frac{x + 4}{x + 1}

Solution steps

\frac{4 - 3 x - x ^{2}}{x ^{2} - 1}

Factor

4 - 3 x - x^{2} : - (x - 1) (x + 4)

= \frac{- ( x - 1 ) ( x + 4 )}{x ^{2} - 1}

Factor

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

= \frac{- ( x - 1 ) ( x + 4 )}{( x + 1 ) ( x - 1 )}

Cancel the common factor:

x - 1

= \frac{- ( x + 4 )}{x + 1}

Apply the fraction rule:

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

= - \frac{x + 4}{x + 1}

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