Answer
$\dfrac{-7x+5}{(x+1)(x-1)}$
Work Step by Step
Using the $LCD=
(x+1)(x-1)
$, the given expression, $
\dfrac{x-2}{x+1}-\dfrac{x-3}{x-1}
,$
\begin{array}{l}\require{cancel}
\dfrac{(x-1)(x-2)-(x+1)(x-3)}{(x+1)(x-1)}
\\\\=
\dfrac{(x^2-2x-x+2)-(x^2+3x+x-3)}{(x+1)(x-1)}
\\\\=
\dfrac{(x^2-3x+2)-(x^2+4x-3)}{(x+1)(x-1)}
\\\\=
\dfrac{x^2-3x+2-x^2-4x+3}{(x+1)(x-1)}
\\\\=
\dfrac{-7x+5}{(x+1)(x-1)}
.\end{array}
