jmc

Notice that the two fractions have the same denominator, so we can add them. Addition is commutative, so we can rearrange the terms to get $$\begin{array}{rl}\frac{k-3}{2}+\frac{3k+1}{2}+3k+1& =\frac{4k-2}{2}+3k+1\\ & =2k-1+3k+1\\ & =\boxed{5k}.\end{array}$$