# How do you simplify (x^2+3x+2)/(x^2-1)?

Apr 8, 2018

$\frac{x + 2}{x + 1}$

#### Explanation:

Factor the numerator and denominator.

For ${x}^{2} + 3 x + 2 ,$ consider two numbers which add up to equal $3$ and multiply to equal $2.$ The numbers $2 , 1$ meet these criteria, so the factored form is

$\left(x + 2\right) \left(x + 1\right)$

For the denominator, recall the Difference of Squares, which tells us that

${x}^{2} - {a}^{2} = \left(x + a\right) \left(x - a\right)$

Thus,

${x}^{2} - 1 = \left(x + 1\right) \left(x - 1\right)$

We then have

$\frac{\left(x + 2\right) \cancel{x + 1}}{\cancel{x + 1} \left(x - 1\right)} = \frac{x + 2}{x + 1}$