Final Answer
$\frac{x-1}{x+3}$
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Step-by-step Solution
Problem to solve:
$\frac{x^2+x-2}{x^2+5x+6}$
Specify the solving method
1
Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$
$\begin{matrix}\left(2\right)\left(3\right)=6\\ \left(2\right)+\left(3\right)=5\end{matrix}$
2
Thus
$\frac{x^2+x-2}{\left(x+2\right)\left(x+3\right)}$
3
Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$
$\begin{matrix}\left(-1\right)\left(2\right)=-2\\ \left(-1\right)+\left(2\right)=1\end{matrix}$
4
Thus
$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$
5
Simplify the fraction $\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$ by $x+2$
$\frac{x-1}{x+3}$
Final Answer
$\frac{x-1}{x+3}$