# Inequality question (when fraction < zero)

## Homework Statement

Solve for t:

[-2(t2+1) / 9(t2-1)] < 0

## The Attempt at a Solution

I know that the answer is -inf<t<-1 and 1<t<inf, but how do I show the calculation to get that answer? When I tried, I narrowed it down to t<root-1, but that's not possible (without complex numbers) and doesn't match the answer???

LCKurtz
Homework Helper
Gold Member
Try factoring the denominator and analyzing the signs of the factors.

So 9(t-1)(t+1), but what do I deduce from that?

LCKurtz
Homework Helper
Gold Member
So 9(t-1)(t+1), but what do I deduce from that?

The sign of a fraction is determined by the signs of its factors. You have a - in front of the fraction and the t2 + 1is always positive. The only places where the denominator changes signs are at 1 and -1. So figure out the signs everywhere else. Wherever you have an even number of negative signs your fraction is negative and an odd number makes it positive.

Ah OK. So it's more by inspection. I would factor as we have done, and then I'd choose for example -2, 0 and 2 and determine the sign giving me the interval values around 1 and -1, correct?

LCKurtz