#### Answer

$2w+5+\frac{10}{w-1}$

#### Work Step by Step

In order to match the first term of the dividend, the divisor must be multiplied by $2w$. The $2w$ will go on top of your division sign.
$$(2w)(w-1)=2w^2-2w$$
Then, subtract this from the first two terms of the dividend
$$(2w^2+3w+5)-(2w^2-2w)=5w$$
Bring down the next term of the dividend
$$5w+5$$
Multiply the divisior by $5$ to match this. The $5$ will follow the $2w$ on top of your division sign.
$$(5)(w-1)=5w-5$$
Subtract this from the dividend.
$$(5w+5)-(5w-5)=10$$
The remainder of 10 can be put over top of the divisor in the answer.