Find the inequalities of 1/x-1<1/x+1

Question

Find out the required set values of x .

Answer 1

This question is ambiguous. There are two possibilities:

(1) 1/(x-1)<1/(x+1)⇒(multiplying through by x²-1) x+1<x-1⇒1<-1 which is FALSE, if x²-1>0, that is, (x-1)(x+1)>0⇒ x-1>0 and x+1>0⇒x>1; or x-1<0 and x+1<0⇒x<-1. If x²-1<0 then -1<x<1, then the inequality is TRUE.

(2) (1/x)-1<(1/x)+1⇒-1<1 which is TRUE for all x.

The most likely answer is (1): -1<x<1, that is, x can be any value between -1 and 1 (exclusively). Example: x=½: -2<⅔; x=-½: -⅔<2.