G(x)=g(x)-g(a)-(x-a)g'(x)

For f (x) and g (x), Cauchy theorem is used in [a, b].

F(b)-F(a) is the left numerator of the equation, and G(b)-G(a) is the left denominator of the equation.

f '(s)= f '(s)-f '(s)+af ' '(s)= af ' '(s)

g '(s)= g '(s)-g '(s)+ag ' '(s)= ag ' '(s)

Substitution into Cauchy theorem is correct.