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

Jun 8, 2018

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

#### Explanation:

We see that the degree of the polynomial in the numerator is larger or equal than the degree of the polynomial in the denominator, so we can divide these two polynomials. After the division we get

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

By factoring the numerator and the denominator we get :

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

or

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

which we can simplify and get :

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

Now if you want to, you can add these to create a single fraction :

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

And you're finished.