Question

How do I solve the rational inequality `(x^2-1)/(x+1)<2` using a TI-83?

Answer 1

You can input `Y1=`function, `Y2=2` and use intercept.

Explanation:

But you can also do this on a piece of paper.
If you factorise the denominator, you get:

`((x-1)cancel((x+1)))/cancel(x+1)<2`

And you can cancel out the `x+1`'s on the condition that `x!=-1` (but that value of `x` was already 'forbidden').

We are now left with: `x-1<2->x<3`

Complete answer: `x<3andx!=-1`
graph{(x^2-1)/(x+1) [-10, 10, -5, 5]}