Question 7537
 At first, two big mistakes you did:
 (I)wrong cateory posting
 (II) missing parenthesis

 Be careful!!!

 f(x)=1/(x^2-2x-8) <0 is equivalent to x^2-2x-8 <0 [since 1 is positive.]

 Solve x^2-2x-8 = (x - 4)(x+2) < 0. 
 [Note two roots 4 & -2 divide the whole real line ibnto 3 parts]

 From the signs in diagram below:     
     +         -        +
  ---------*--------*----------
           -2       4
 
 The solution set : (-2, 4)

 Here,I give you the simplest way to solve this kind of questions.
 Try to read and think carefully about every step.
 No further explanations will be given.

 Kenny