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

May 15, 2018

(x²+3x+2)/(x²-1)=(x+2)/(x-1)

#### Explanation:

(x²+3x+2)/(x²-1)
$= \frac{\cancel{\left(x + 1\right)} \left(x + 2\right)}{\left(x - 1\right) \cancel{\left(x + 1\right)}}$
$= \frac{x + 2}{x - 1}$

May 15, 2018

First we should split the middle term

By the video... you should have understood that we need to make $3 x$ in two number that one is divisible by 2 and the other is divisible itself

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

You should always remember that
$1 = {1}^{2}$
$\frac{x \left(x + 1\right) + 2 \left(x + 1\right)}{{x}^{2} - {1}^{2}}$
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$
$\frac{\left(x + 2\right) \cancel{\left(x + 1\right)}}{\left(x - 1\right) \cancel{\left(x + 1\right)}}$
$\frac{x + 2}{x - 1}$