what is the simplest form of this expression?
x-3/x-1 + 6/x-3
A. x^2+12x+15/(x-1)(x-3)
B. x^2-6x+3/(x-1)(x-3)
C. x^2+3/(x-1)(x-3)
D. x+3/(x-1)(x-3)
+53 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.
