Answer
$\dfrac{-2x+5}{2(x+1)}$
Work Step by Step
Factoring the given expression, $
\dfrac{2}{x+1}-\dfrac{3x}{3x+3}+\dfrac{1}{2x+2}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{2}{x+1}-\dfrac{3x}{3(x+1)}+\dfrac{1}{2(x+1)}
.\end{array}
Using the $LCD=
6(x+1)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{6(2)-2(3x)+3(1)}{6(x+1)}
\\\\=
\dfrac{12-6x+3}{6(x+1)}
\\\\=
\dfrac{-6x+15}{6(x+1)}
\\\\=
\dfrac{3(-2x+5)}{3\cdot2(x+1)}
\\\\=
\dfrac{\cancel{3}(-2x+5)}{\cancel{3}\cdot2(x+1)}
\\\\=
\dfrac{-2x+5}{2(x+1)}
.\end{array}
