Which of the following is equivalent to the expression below for x≠6?

2x²-18x+36/x-6

2 (x+3)

2x-3

2x+3

2 (x-3)

The fourth answer choice is the correct one: 2 (x - 3)

Step-by-step explanation:

2x²-18x+36/x-6 should be factored, as follows:

2 (x²-9x+18) / (x-6) = 2 (x - 3) (x - 6) / (x - 6)

Substituting x = 6 would result in division by zero and is thus not allowed.

Remembering this, we can reduce 2 (x - 3) (x - 6) / (x - 6) to 2 (x - 3) for x≠6.