So I'm just about done with my latest assignment, however there's this little vermin impeding my way towards a perfect score. I think I may have nailed the answer, but given that it's my last available attempt at submitting a response, I want to beextrasure.

Some background information before the actual question:

The function...

The expression is defined exactly on the set...

The expression is equal to zero if is equal to...

The set of all real numbers for which is defined and non-zero is...

And so, here is what's currently holding me back...

By analyzing the sign of on the above open intervals, solve the inequality...

... expressing answer in interval notation.

My answer to this was:

Is it correct?