Simplify $\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$.
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{align*}
\frac{k-3}{2} +\frac{3k+1}{2}+3k+1 &=\frac{4k-2}{2}+3k+1 \\
&=2k-1+3k+1 \\
&=\boxed{5k}.\end{align*}