Let's solve your inequality step-by-step.
x2+9x−22/x+4 >0
Let's find the critical points of the inequality.
x2+9x−22/x+4 =0
x2+9x−22=0(Multiply both sides by x+4)
(x−2)(x+11)=0(Factor left side of equation)
x−2=0 or x+11=0(Set factors equal to 0)
x=2 or x=−11
Check possible critical points.
x=2(Works in original equation)
x=−11(Works in original equation)
Critical points:
x=2 or x=−11(Makes both sides equal)
x=−4(Makes left denominator equal to 0)
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<−11(Doesn't work in original inequality)
−11<x<−4(Works in original inequality)
−4<x<2(Doesn't work in original inequality)
x>2(Works in original inequality)
Answer:
<em>−11<x<−4 or x>2~</em>
