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.