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

Jul 8, 2015

You can input $Y 1 =$function, $Y 2 = 2$ and use intercept.

Explanation:

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

$\frac{\left(x - 1\right) \cancel{\left(x + 1\right)}}{\cancel{x + 1}} < 2$

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

We are now left with: $x - 1 < 2 \to x < 3$

Complete answer: $x < 3 \mathmr{and} x \ne - 1$
graph{(x^2-1)/(x+1) [-10, 10, -5, 5]}