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How do you (4x^2-3x+1)/(x^4-x^2) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
   2          
4*x  - 3*x + 1
--------------
    4    2    
   x  - x     
$$\frac{\left(4 x^{2} - 3 x\right) + 1}{x^{4} - x^{2}}$$
(4*x^2 - 3*x + 1)/(x^4 - x^2)
Fraction decomposition [src]
1/(-1 + x) - 1/x^2 - 4/(1 + x) + 3/x
$$- \frac{4}{x + 1} + \frac{1}{x - 1} + \frac{3}{x} - \frac{1}{x^{2}}$$
  1      1      4     3
------ - -- - ----- + -
-1 + x    2   1 + x   x
         x             
General simplification [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
Numerical answer [src]
(1.0 + 4.0*x^2 - 3.0*x)/(x^4 - x^2)
(1.0 + 4.0*x^2 - 3.0*x)/(x^4 - x^2)
Trigonometric part [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
Powers [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
Common denominator [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
Combining rational expressions [src]
1 + x*(-3 + 4*x)
----------------
   2 /      2\  
  x *\-1 + x /  
$$\frac{x \left(4 x - 3\right) + 1}{x^{2} \left(x^{2} - 1\right)}$$
(1 + x*(-3 + 4*x))/(x^2*(-1 + x^2))
Assemble expression [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
Combinatorics [src]
                2  
   1 - 3*x + 4*x   
-------------------
 2                 
x *(1 + x)*(-1 + x)
$$\frac{4 x^{2} - 3 x + 1}{x^{2} \left(x - 1\right) \left(x + 1\right)}$$
(1 - 3*x + 4*x^2)/(x^2*(1 + x)*(-1 + x))
Rational denominator [src]
             2
1 - 3*x + 4*x 
--------------
    4    2    
   x  - x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)