Verify if 2x-1/(x^2+1) = f(x) if f(x) = (2x^3+2x-1)/(x^2+1)

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We'll choose to re-write f(x):

( 2x^3 + 2x - 1 )/ (x^2 + 1) = (2x^3 + 2x)/(x^2 + 1) - 1/(x^2 + 1)

We'll factorize by 2x the first fraction:

(2x^3 + 2x)/(x^2 + 1) = 2x(x^2 + 1)/(x^2 + 1)

We'll reduce the first fraction:

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

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

We notice that re-writing f(x) we've get the 1st given expression of f(x).Therefore, 2x - 1/(x^2 + 1) = ( 2x^3 + 2x - 1 )/ (x^2 + 1).** **

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