Answer:
The required numerator is 2x²-14x+12 OR 2(x-1)(x-6)
Explanation:
Considering the equivalent of the ratio of numerator and denominator to be 2/(x-2), we have to find numerator for given denominator.
Let numerator is A:
then:

cancelling (x-2) from both sides:

Multiplying numerator of A on left side:

Hence,
The required numerator is 2x²-14x+12 OR 2(x-1)(x-6)