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: $\frac{A}{(x-2)(x-1)(x-6)}$

If $\frac{2}{x-2} =\frac{A}{(x-2)(x-1)(x-6)}$,
then: $A = \frac{2(x-2)(x-1)(x-6)}{(x-2)}$

(x-2) can be cancelled: $A = \frac{2(x-2)(x-1)(x-6)}{(x-2)}= 2(x-1)(x-6)$

Answer 2

Answer:

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

Step-by-step 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:

$\frac{2}{x-2}=\frac{A}{(x-2)(x-1)(x-6)}  $

cancelling (x-2) from both sides:

$2=\frac{A}{(x-1)(x-6)}$

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)