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.

There is no correct answer. Perhaps you made a typo on (A)?

At any rate, the best way to solve problems such as these is usually to run a scenario.

Let x = 3
So the numerator works out to 3(2)-2(4)+3(8) = 22 and the denominator will be (3-1) = 2.

So when x=3 our target answer is 22/2

Answer choice (A) works out to (3)(3)+13 / 4 = 22/4 . This doesn't match the target answer.