Solution - Simplification or other simple results

Step  1  :

              2x  
 Simplify   ——————
            x2 + 1

Polynomial Roots Calculator :

 1.1    Find roots (zeroes) of :       F(x) = x² + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  1  :

   d     2x  
  —— • ——————
  dx   x2 + 1

Step  2  :

             d
 Simplify   ——
            dx

Canceling Out :

 2.1    Canceling out d as it appears on both sides of the fraction line

Equation at the end of step  2  :

  1     2x  
  — • ——————
  x   x2 + 1

Step  3  :

Canceling Out :

 3.1    Canceling out x as it appears on both sides of the fraction line

Final result :

     2  
  ——————
  x2 + 1