Problem Solving

If x ≠ 1, which expression is equal to
$$\frac{x\left(x-1\right)-2\left(x+1\right)+3\left(x+5\right)}{\left(x-1\right)}=?$$

$$A.\ \frac{x^2+13}{\left(x-1\right)}$$
$$B.\ \frac{x^2+17}{\left(x-1\right)}$$
$$C.\ \frac{x^2+x+12}{\left(x-1\right)}$$
$$D.\ \frac{x^2+x+5}{\left(x-1\right)}$$
$$E.\ \frac{13}{\left(x-1\right)}$$

The OA is A.

Experts, in this PS question, I need to expand the numerator of the expression and get the answer, right?

Then,
$$\frac{x^2-x-2x-2+3x+15}{\left(x-1\right)}=\frac{x^2+13}{\left(x-1\right)}$$
Thanks.