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How do you x^4/(x^2+1) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
   4  
  x   
------
 2    
x  + 1
$$\frac{x^{4}}{x^{2} + 1}$$
x^4/(x^2 + 1)
Fraction decomposition [src]
-1 + x^2 + 1/(1 + x^2)
$$x^{2} - 1 + \frac{1}{x^{2} + 1}$$
      2     1   
-1 + x  + ------
               2
          1 + x 
Numerical answer [src]
x^4/(1.0 + x^2)
x^4/(1.0 + x^2)
Common denominator [src]
      2     1   
-1 + x  + ------
               2
          1 + x 
$$x^{2} - 1 + \frac{1}{x^{2} + 1}$$
-1 + x^2 + 1/(1 + x^2)