# How do I solve the rational inequality (x^2-x-6)/(x+2)<=-3 using a TI-83?

Oct 19, 2014

If you do not have to use a calculator, then here is how.

By factoring out the numerator,

$\frac{\left(x + 2\right) \left(x - 3\right)}{x + 2} \le - 3$

by cancelling out $\left(x + 2\right)$'s,
(Note that $x \ne - 2$ since we cannot have a zero denominator.)

$R i g h t a r r o w x - 3 \le - 3$

by adding $3$,

$R i g h t a r r o w x \le 0$

Hence, the solution set of the inequality is

$\left(- \infty , - 2\right) \cup \left(- 2 , 0\right]$.

I hope that this was helpful.