help me with this one!

Question

f(x)=log(1+x)/(1-x) and g(x)=(3x+x²)/(3x²+1) 

prove that (fοg)(x)=3f(x)

Answer 1

show (fog)(x) = 3f(x) is an identity. check to see if it is, try x=1/2

f(1/2) = log(3/2/1/2) = log3, 3f(3) = 3log3 = log27

g(1/2) =(3x+x^2)/(3x^2+1) =(3/2+1/4)/(3/4 +1) = 7/4/7/4 = 1

f(g(1/2) = f(1) = log(2/0) which doesn't = log27

(fog)(x) = f(g(x)) = f((3x+x^2)/(3x^2+1)) = log((1+(3x+x^2)/(3x^2+1))/(1-(3x+x^2)/(3x^2+1))

3f(x) = log((1+x)^3/(1-x)^3)= 3log(1+x) - 3log(1-x)

no apparent way to show 3log(1+x) -3log(1-x) = log(1+(3x+x^2)/(3x^2+1)/(1-(3x+x^2)/3x^2+1))