Carcass wrote:
For which of the following values of \(x\) does \(\frac{x-5}{x-2}\) have the greatest value?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 5
Let's plug each answer choice into the given expression...
(A) \(\frac{x-5}{x-2}=\frac{0-5}{0-2}=\frac{-5}{-2}=2.5\)
(B) \(\frac{x-5}{x-2}=\frac{1-5}{1-2}=\frac{-4}{-1}=4\)
(C) \(\frac{x-5}{x-2}=\frac{3-5}{3-2}=\frac{-2}{1}=-2\)
(D) \(\frac{x-5}{x-2}=\frac{4-5}{4-2}=\frac{-1}{2}=-0.5\)
(E) \(\frac{x-5}{x-2}=\frac{5-5}{5-2}=\frac{0}{3}=0\)
Answer: B