help. expressions

We want $\frac{x-3}{x-1}+\frac{ 6}{x-3}$. finding common denominator, we get $\frac{(x-3)^2+6(x-1)}{(x-3)(x-1)}$

Using distrubutive property and combining like terms about a billion times later, we get $\frac{x^2+3}{(x-1)(x-3)}$, thus $\text{C}$ is the correct answer choice.