Question 1020598

Could someone please help me solve a rational inequality using the critical point method?  1/x+2>x+2. I know how to use the critical point method, but I am not sure how to get the problem in the correct form first? I appreciate any help you can give me!
<pre>{{{1/(x + 2) > x + 2}}}, with {{{x <> - 2}}}
1 = (x + 2)(x + 2) ---- Multiplying each side by LCD, x + 2, and changing INEQUALITY to equality
{{{1 = x^2 + 4x + 4}}}
{{{0 = x^2 + 4x + 3}}} --------- Subtracting 1 from each side
{{{x^2 + 4x + 3 = 0}}} --------- Reversing sides
(x + 3)(x + 1) = 0
x + 3 = 0         OR       x + 1 = 0
x = - 3           OR       x = - 1 

Thus, the 3 CRITICAL points are: - 2, - 3, and - 1. Arranged in numerical order, this
becomes: - 3, - 2, - 1. From these 3 CRITICAL points, the following 4 intervals have to be tested:
      x < - 3, or x = - 4
- 3 < x < - 2, or x = - 2.5
- 2 < x < - 1, or x = - 1.5
      x > - 1, or x = 0 
When the above intervals are tested, we find that: {{{highlight(highlight_green(highlight(matrix(2,1,x < - 3,- 2 < x < - 1))))}}}, are TRUE, and so, these are the solutions. 
The other 2 intervals make the INEQUALITY false, so they're not solutions.