Answer
$\dfrac{y-3}{x+2}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{xy-3x+2y-6}{x^2+4x+4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(xy-3x)+(2y-6)}{x^2+4x+4}
\\\\=
\dfrac{x(y-3)+2(y-3)}{(x+2)(x+2)}
\\\\=
\dfrac{(y-3)(x+2)}{(x+2)(x+2)}
\\\\=
\dfrac{(y-3)(\cancel{x+2})}{(x+2)(\cancel{x+2})}
\\\\=
\dfrac{y-3}{x+2}
.\end{array}
