First, find your "zeroes". We know that the denominator cannot equal 0 so
x² ≠ 0 → x ≠ 0
Next, multiply both sides by x² to clear the denominator (since x² will always be positive, the inequality sign will not change). This leaves you with:
|x + 2| - |x - 3| > -x²
Change the inequality symbol to an equal sign and solve for all possibilities: (x+2) - (x-3) = -x² → imaginary number
(x+2) - -(x-3) = -x² → x = -1 + √2, x = -1 - √2
-(x+2) - (x-3) = -x² → x = 1
-(x-2) - -(x-3) = -x² → x = √5, x = -√5
Now, find Test Points between all of the values above to see which makes a TRUE statement with the original inequality.
Answer: x < -√5 or x > -1 + √2
