#### Answer

$-\dfrac{4}{x-1}$

#### Work Step by Step

Subtracting the numerators and copying the denominator, the given expression, $
\dfrac{5-3x}{x^2-2x+1}-\dfrac{x+1}{x^2-2x+1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5-3x-(x+1)}{x^2-2x+1}
\\\\=
\dfrac{5-3x-x-1}{x^2-2x+1}
\\\\=
\dfrac{4-4x}{x^2-2x+1}
\\\\=
\dfrac{4(1-x)}{(x-1)(x-1)}
\\\\=
\dfrac{-4(x-1)}{(x-1)(x-1)}
\\\\=
\dfrac{-4(\cancel{x-1})}{(x-1)(\cancel{x-1})}
\\\\=
\dfrac{-4}{x-1}
\\\\=
-\dfrac{4}{x-1}
.\end{array}