Answer
$\frac{3x-1}{2x+1}$
Work Step by Step
We simplify as follows:
$\frac{2(x-1)^{-1}+3}{3(x-1)^{-1}+2}$
$=\frac{\frac{2}{x-1}+\frac{3(x-1)}{x-1}}{\frac{3}{x-1}+\frac{2(x-1)}{x-1}}$
$=\frac{2+3(x-1)}{3+2(x-1)}$
$=\frac{3x-1}{2x+1}$
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