What is (x^2-9)/(x^2+5x+6) ?

The solution to (x^2-9)/(x^2+5x+6) is (x-3)/(x+2)

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simplify (x^2-9)/(x^2+5x+6)

simplify

\frac{x ^{2} - 9}{x ^{2} + 5 x + 6}

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

Solution steps

\frac{x ^{2} - 9}{x ^{2} + 5 x + 6}

Factor

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

= \frac{( x + 3 ) ( x - 3 )}{x ^{2} + 5 x + 6}

Factor

x^{2} + 5 x + 6 : (x + 2) (x + 3)

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

Cancel the common factor:

x + 3

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

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

\frac{x ^{2} - 3 x - 18}{x ^{2} - 15 x + 54}

\frac{7}{8} + \frac{7}{10}

- 2 x^{2} - 2

(6 - 35)^{2}