Answer
$[-1,2)$
Work Step by Step
To solve the nonlinear inequality $\frac{x+1}{x-2}\leq $ first observe that the numbers $-1$ and $2$ are zeros of the numerator and denominator. These numbers divide the real line into three intervals:
$ (-\infty,-1), (-1,2), and (2,\infty)$
The endpoint $-1$ satisfies the inequality, because $\frac{-1 + 1}{-1 - 2}=0\leq0$,
but $2$ fails to satisfy the inequality because $\frac{2+1}{2-2}$ is not defined.
Thus, referring to the table, we see that the solution of the inequality is $[-1,2)$.
