# How do you evaluate the limit of #lim (2x^2+5x+2)/(x^2+x-2)# as #x->-2#?

##### 1 Answer

Dec 16, 2016

#### Explanation:

Start by factoring, because we are currently in indeterminate form

#=lim_(x->-2) (2x^2 + 4x + x+ 2)/((x+ 2)(x- 1))#

#=lim_(x-> -2) (2x(x + 2) + 1(x + 2))/((x + 2)(x - 1))#

#=lim_(x-> -2) ((2x+ 1)(x + 2))/((x +2)(x - 1))#

#= lim_(x-> -2) (2x + 1)/(x- 1)#

We can now evaluate.

#= (2(-2) + 1)/(-2 - 1)#

#=(-3)/(-3)#

#=1#

Hopefully this helps!