What is (x^2+5x+6)/(x^2-4) ?

The solution to (x^2+5x+6)/(x^2-4) is (x+3)/(x-2)

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simplify (x^2+5x+6)/(x^2-4)

simplify

\frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

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

Solution steps

\frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

Factor

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

= \frac{( x + 2 ) ( x + 3 )}{x ^{2} - 4}

Factor

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

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

Cancel the common factor:

x + 2

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

(- 7 x) (- 2 x) (- 3 x^{4})

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

50 x^{3}

\frac{3 x}{2 x}