Help Finding Concave up of a large rational function

Greetings.

f(x)= (x^2-4)/(x^2+3x+2)
f'(x)= (3x^2+12x+12)/(x^4+6x^3+13X^2+12X+4)
f''(x)= (-12x^5-42x^4-6x^3+120x^2+48)/(x^8+6x^7+13x^6+12x^5+4x^4)

So far I have:

x Int= (-2,0)
Horizontal Asymptote= 1
Vertical Asymptote= Does Not Exist

I need f(x) is concave up on the interval(s)=

As you can see the double prime is nasty, and I don't know how to simplify it in order to help me find the concave up intervals. Any help or direction would be appreciated.

Thank you.

Try to simplify f: .