Answer
No solution.
Work Step by Step
$\log_3(x-1) - \log_3(x+2) = 2$
$\log_3 \frac{x-1}{x+2} = 2$
$3^{2} = \frac{x-1}{x+2}$
$9 = \frac{x-1}{x+2}$
$9(x+2) = x-1$
$9x + 18 = x -1 $
$9x - x = -1 - 18$
$8x = - 19$
$x = \frac{-19}{8}$
No solution.