Having trouble solving a 3 marks question

Question

Simplify fully:

$$\frac{3x^2 - 8x - 3} { 2x^2 - 6x}$$

And the answer needs to be $12(x^2 + 1)$

EDIT: Seems like the answer was wrong but I wasn't confident enough to say it. Blaming my teacher for this now. Thank you for the help!

Answer 1

$$\frac{(3x^2 - 8x - 3)}{(2x^2 - 6x)}=\frac{(3x+1)(x-3)}{2x(x-3)}=\frac{3x+1}{2x}$$

I think your answer is wrong.

Answer 2

Note that $$3x^2-8x-3=(3x+1)(x-3)$$

Answer 3

Hint: (Although the answer is wrong).

You can either prove that $\frac{P(x)}{Q(x)}=R(X)$ where $P(x), Q(x)$ and $R(x)$ are polynomials with the polynomial division or if you know the answer (as in this case), you might want to prove that $$R(x)·Q(x)=P(x)$$ which is equivalent to $$\frac{P(x)}{Q(x)}=R(X)$$ whenever $Q(x)≠0.$