interval notation and inequalities

Question

Solve and write the answer in interval notation. x-1/x+2 >2

 

Please explain the steps you took to get the answer

Thanks!

Answer 1

(x-1)/(x+2) > 2

 

(x-1)/(x+2) - 2 > 0

 

[(x-1)-2(x+2)]/(x+2) > 0

 

(-x-5)/(x+2) > 0

 

numerator = 0 when x = -5   denominator = 0 when x = -2

 

__________l____________l__________

               -5                  -2

 

When x < -5, (-x-5)/(x+2) < 0

When -5<x<-2, (-x-5)/(x+2) > 0

When x>-2, (-x-5)/(x+2) < 0

 

Solution set:  -5 < x < -2    Interval notation:  (-5,-2)