lim x-> infinity [ |9+5x-6x^2| ] / [ 2x^2 - xsinx ]

i get 0 as answer. Firstly I used Hopital rule, and then i factor out x^2 before getting 0 as answer. But i think im wrong, can any one help?

I did not just factor out x^2 initially, because if i do that, for the xsinx term in the denominator, it becomes (sinx)/x. And if you take x-> infinity to (sinx)/x, doesnt it give u infinity/infinity and not 0?