Given the following find the function g Fx 1x fg x x6x2 x

Given the following, find the function g. F(x) = 1/x (f/g) (x) = x+6/x^2 - x g(x) =

f(x)=1/x

(f/g)(x)=(x+6)/(x² -x)

(f/g)(x)=f(x)/g(x)

f(x)/g(x)=(x+6)/(x² -x)

f(x)/g(x)=(x+6)/(x(x -1))

(1/x)/g(x)=(x+6)/(x(x -1))

1/g(x)=(x+6)/(x -1)

g(x)=(x -1)/(x+6)