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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)

 Sep 2, 2022
edited by Guest  Sep 2, 2022
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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.

 Sep 3, 2022

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