Answer
w=3
Work Step by Step
$\frac{w^2+3}{2w+2}=\frac{w}{2}$ cross multiply
$2(w^2+3)=w(2w+2)$ distributive property
$2w^2+6=2w^2+2w$ subtract $2w^2$ from each side
$2w^2+6-2w^2=2w^2+2w-2w^2$ combine like terms
$6=2w$ divide both sides by 2
$6\div2=2w\div2$ simplify
$3=w$
