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

2/(x-2)

2 Answers

5 votes
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)



User Cchristelis
by
7.1k points
1 vote

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:


(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)

User Alexandra Masse
by
6.5k points