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

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We have to findx given that fof(x)=0 and f(x)=1/(x^2+x).

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

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

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

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

Now this is equal to zero

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

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

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

So we get x = 0 and x = -1

Therefore x= 0 and x = -1.

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