Question

Please show that

1/(g o f)(x) - 1-(g o f)(x)/(g o f)(x) = 1

Answer 1

I don't know what your (gof)(x) is supposed to mean, so let's just call it Y.

You are asking for a proof that
1/Y - (1-Y)/Y = 1
1/Y - 1/Y + Y/Y = 1
1 = 1

There is your proof