Answer
See below
Work Step by Step
$$\frac{2}{x-3}-\frac{1}{x+2}=\frac{x-5}{x+2}\\\frac{2}{x-3}=\frac{x-4}{x+2}\\x^2-7x+12=2x+4\\x^2-9x+8=0\\(x-1)(x-8)=0\\x=1 \lor x=8$$
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