# Step-by-step Solution

## Simplify the expression $\frac{x^2+x-2}{x^2+5x+6}$

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### Videos

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

## Step-by-step explanation

Problem to solve:

$\frac{x^2+x-2}{x^2+5x+6}$
1

Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$

$\begin{matrix}\left(-1\right)\left(2\right)=-2\\ \left(-1\right)+\left(2\right)=1\end{matrix}$
2

Thus

$\frac{\left(x-1\right)\left(x+2\right)}{x^2+5x+6}$
3

Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$

$\begin{matrix}\left(2\right)\left(3\right)=6\\ \left(2\right)+\left(3\right)=5\end{matrix}$
4

Thus

$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$
5

Simplifying

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

$\frac{x-1}{x+3}$
$\frac{x^2+x-2}{x^2+5x+6}$