Differentiate. G(x)= (6-(1/x)) / (x-2)

We'll note G(x) = y

dy/dx =
d/dx {[6-(1/x)] / (x-2)}

dy/dx = d/dx [6/(x-2)] - d/dx
[1/x(x-2)]

d/dx [6/(x-2)] = [(x-2)*d/dx(6) -
6*d/dx(x-2)]/(x-2)^2

d/dx [6/(x-2)] = [0*(x-2) -
6*1]/(x-2)^2

d/dx [6/(x-2)] = - 6/(x-2)^2
(1)

d/dx [1/x(x-2)] = d/dx
[1/(x^2-2x)]

d/dx [1/(x^2-2x)] = [(x^2-2x)*d/dx(1) -
1*d/dx(x^2-2x)]/x^2*(x-2)^2

d/dx [1/(x^2-2x)] =
-(2x-2)/x^2*(x-2)^2 (2)

dy/dx = (1) -
(2)

dy/dx = - 6/(x-2)^2 +
(2x-2)/x^2*(x-2)^2

dy/dx = (2x - 2 -
6x^2)/x^2*(x-2)^2

dG/dx =
2(x-1-3x^2)/x^2*(x-2)^2