Answer
$b+6+\frac{25}{2b+4}$
Work Step by Step
Re-arranging the order of the terms, the given is equivalent to
$$
(2b^2+16b+49)\div(2b+4)
.$$
Using the long division method shown below, then
$$\begin{aligned}
&(2b^2+16b+49)\div(2b+4)
\\&=
b+6+\frac{25}{2b+4}
.\end{aligned}$$
