Question

Give the equivalent numerator if the denominator is (x - 2)(x - 1)(x - 6).

2/(x-2)

Answer 1

The answer is 2(x - 1)(x - 6)

Let A be the equivalent numerator:
`(A)/((x-2)(x-1)(x-6))`

If
`(2)/(x-2) =(A)/((x-2)(x-1)(x-6))`,
then:
`A = (2(x-2)(x-1)(x-6))/((x-2))`

(x-2) can be cancelled:
`A = (2(x-2)(x-1)(x-6))/((x-2))= 2(x-1)(x-6)`

Answer 2

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:

`(2)/(x-2)=(A)/((x-2)(x-1)(x-6))  \\`

cancelling (x-2) from both sides:

`2=(A)/((x-1)(x-6))`

Multiplying numerator of A on left side:

`2(x-1)(x-6)=A\\2(x^(2)-7x+6)=A\\2x^(2)-14x+12=A`

Hence,

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