Problem Solving

For all numbers x such that x != 1 (NOT EQUAL), if g(x) is defined by g(x) = (x^2 + 2) / (x - 1), then (1/g(2)) * (1/g(x)) =

Answer is (x-1)/6(x^2 + 2) according to GMat I just need some1 to help me understand how they got that.

I did this, (6/1) * (1 / ( (x^2 + 2)/(x - 1) ) = (6x + 6) / (x^2 +2) ,,,, no?

moatik wrote:For all numbers x such that x != 1 (NOT EQUAL), if g(x) is defined by g(x) = (x^2 + 2) / (x - 1), then (1/g(2)) * (1/g(x)) =

Answer is (x-1)/6(x^2 + 2) according to GMat I just need some1 to help me understand how they got that.

I did this, (6/1) * (1 / ( (x^2 + 2)/(x - 1) ) = (6x + 6) / (x^2 +2) ,,,, no?

Hi!

You made a couple of errors.

First, the first term is 1/g(2), not g(2). So, subbing in:

1/g(2) = 1/(6/1) = 1/6

and the second term is:

1/g(x) = 1/((x^2 + 2) / (x - 1)) = (x-1)/(x^2 + 2)

Taking the product of those two terms:

(1/6)*(x-1)/(x^2 + 2)

= (1)(x-1)/(6)(x^2 + 2)

= (x-1)/6(x^2 + 2)

which is what you posted as the accredited answer.

Hope that helps!