How do you simplify $\frac{x + 3}{x^{2} + 5 x + 6}$ $(x + 3)/(x^2 + 5x + 6)$ ?

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Answer 1 · 2015-05-30T22:51:52

$x^{2} + 5 x + 6 = (x + 2) (x + 3)$ $x^2+5x+6 = (x+2)(x+3)$

So

$(x+3)/(x^2+5x+6) = cancel(x+3)/((x+2)cancel((x+3))) = 1/(x+2)$

...provided $x != -3$ (and $x != -2$ )

How do you simplify (x + 3)/(x^2 + 5x + 6)x+3x2+5x+6(x + 3)/(x^2 + 5x + 6)?