f(x)= X^2 + X, h(x)= X/1-X....Find h(f(x)) in terms of X.

Given the functions f(x) and h(x) such
that:

f(x) = x^2 + x

h(x) = x /
(1-x).

We need to find h(f(x))

To find
h(f(x) we will substitute with f(x) in g(x).

h(f(x)) = h ( x^2 +
x)

Now substitute with  (x^2 + x) in
h(x):

            = ( x^2 + x) / ( 1- (x^2 +
x)

Now we will simplify.

Factor x from
the numerator.

             = x( x+1) / (1-x^2 -
x)

               = - x(x+1) / ( x^2 + x
-1)

==> h(f(x)) = -x(x+1)/ (x^2 +x -1)