(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all x for which [itex]\frac{x-1}{x+1}>0 \qquad(1)[/itex]

2. Relevant equations

(2) AB > 0 if A,B >0 OR A,B < 0

(3) 1/Z > 0 => Z > 0

3. The attempt at a solution

Since (1) holds if:

[itex] (x-1) > 0 \text{ and } (x+1) > 0 \qquad x\ne -1[/itex]

then we must have x>1 AND x>-1

and since (1) also will hold if:

[itex] (x-1) < 0 \text{ and } (x+1) < 0 \qquad x\ne -1[/itex]

then we must have x<1 AND x<-1

So that the solution is x on the interval [itex](-\infty,-1) \cup (1,\infty)[/itex].

What is the proper way to write the solution using set builder notation?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Spivak 4 (xiv): Inequality

**Physics Forums | Science Articles, Homework Help, Discussion**