Given the ration expression 12x^2-108/36x-108, which of the following represents its simplest form?
A. 12(x+3)/36
B. x+3/3
C. x/3
D. x^2-9/3(x-3)
To simplify the given rational expression, we need to factor the numerator and denominator first:
12x^2 - 108 = 12(x^2 - 9) = 12(x - 3)(x + 3)
36x - 108 = 36(x - 3)
So, our simplified form of the rational expression is:
(12(x - 3)(x + 3)) / (36(x - 3))
Now we can cancel out the common factors of (x - 3) in the numerator and denominator:
(12(x + 3)) / 36
Simplifying further, we divide both the numerator and denominator by 12:
(x + 3) / 3
Therefore, the correct answer is:
B. x + 3 / 3