What is (9-x^2)/(x^2-2x-3) ?

The solution to (9-x^2)/(x^2-2x-3) is -(3+x)/(x+1)

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simplify (9-x^2)/(x^2-2x-3)

simplify

\frac{9 - x ^{2}}{x ^{2} - 2 x - 3}

- \frac{3 + x}{x + 1}

Solution steps

\frac{9 - x ^{2}}{x ^{2} - 2 x - 3}

Factor

9 - x^{2} : (3 + x) (3 - x)

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

Factor

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

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

(3 + x) (3 - x) = - (3 + x) (x - 3)

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

Cancel the common factor:

x - 3

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

Apply the fraction rule:

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

= - \frac{3 + x}{x + 1}

\frac{9}{5} 10 + 32

\frac{x ^{2}}{2 x y}

\frac{1}{1} - \frac{3}{4}

\frac{4 x ^{4} + 8 x ^{3} + 16 x ^{2}}{4 x ^{2}}

4 \frac{2}{3} - 2 \frac{3}{5}