Solve the equation fof(x)=0 Where f(x)=1/(x^2+x)

(fof)(x) = f(f(x))

We'll
substitute x by f(x) and we'll get:

f(f(x)) =
1/[f^2(x)+f(x)]

f(f(x)) = 1/[1/(x^2+x)^2 +
1/(x^2+x)]

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

We'll put f(f(x)) =
0:

(x^2+x)^2/(1 + x + x^2) =
0

Since the denominator is always positive, we'll put the
numerator as zero:

(x^2+x)^2 =
(x^2+x)(x^2+x)

(x^2+x)^2 =
0

(x^2+x)(x^2+x) = 0

We'll
factorize by x both brackets:

x*x(x+1)(x+1) =
0

x1 = 0 and x2 =
0

x + 1 =
0

x3 = -1 and x4 =
-1

The solutions of the
equation (fof)(x) = 0 are {-1 ; 0}.