# How do you simplify ((x-3)/(x^2+3x+2))/((x^2-9)/(x+1))?

May 5, 2017

I tried this:

#### Explanation:

We can write it rearranging:

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

where we changed the fraction into a multiplication.

We may now simplify:

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

and be left with:

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