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Expression simplification/ Fraction Decomposition into the simple/ ((z^2+1)^2/(4*z^2))/(13+12*((z^2+1)/2*z*z))

How do you ((z^2+1)^2/(4*z^2))/(13+12*((z^2+1)/2*z*z)) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
   /        2\    
   |/ 2    \ |    
   |\z  + 1/ |    
   |---------|    
   |      2  |    
   \   4*z   /    
------------------
         2        
        z  + 1    
13 + 12*------*z*z
          2
$$\frac{\frac{1}{4 z^{2}} \left(z^{2} + 1\right)^{2}}{12 z z \frac{z^{2} + 1}{2} + 13}$$ 
((z^2 + 1)^2/((4*z^2)))/(13 + 12*((((z^2 + 1)/2)*z)*z))
General simplification [src] 
              2      
      /     2\       
      \1 + z /       
---------------------
    4       6       2
24*z  + 24*z  + 52*z
$$\frac{\left(z^{2} + 1\right)^{2}}{24 z^{6} + 24 z^{4} + 52 z^{2}}$$ 
(1 + z^2)^2/(24*z^4 + 24*z^6 + 52*z^2)
Fraction decomposition [src] 
1/(52*z^2) + (20 + 7*z^2)/(52*(13 + 6*z^2 + 6*z^4))
$$\frac{7 z^{2} + 20}{52 \left(6 z^{4} + 6 z^{2} + 13\right)} + \frac{1}{52 z^{2}}$$ 
                      2      
  1           20 + 7*z       
----- + ---------------------
    2      /        2      4\
52*z    52*\13 + 6*z  + 6*z /
Expand expression [src] 
                2        
        / 2    \         
        \z  + 1/         
-------------------------
     /         2        \
   2 |        z  + 1    |
4*z *|13 + 12*------*z*z|
     \          2       /
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(12 z z \frac{z^{2} + 1}{2} + 13\right)}$$ 
(z^2 + 1)^2/(4*z^2*(13 + 12*((((z^2 + 1)/2)*z)*z)))
Assemble expression [src] 
                2         
        /     2\          
        \1 + z /          
--------------------------
     /           /     2\\
   2 |         2 |1   z ||
4*z *|13 + 12*z *|- + --||
     \           \2   2 //
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(12 z^{2} \left(\frac{z^{2}}{2} + \frac{1}{2}\right) + 13\right)}$$ 
(1 + z^2)^2/(4*z^2*(13 + 12*z^2*(1/2 + z^2/2)))
Rational denominator [src] 
                2        
        /     2\         
        \1 + z /         
-------------------------
   2 /         2       4\
2*z *\26 + 12*z  + 12*z /
$$\frac{\left(z^{2} + 1\right)^{2}}{2 z^{2} \left(12 z^{4} + 12 z^{2} + 26\right)}$$ 
(1 + z^2)^2/(2*z^2*(26 + 12*z^2 + 12*z^4))
Common denominator [src] 
         4      2    
    1 + z  + 2*z     
---------------------
    4       6       2
24*z  + 24*z  + 52*z
$$\frac{z^{4} + 2 z^{2} + 1}{24 z^{6} + 24 z^{4} + 52 z^{2}}$$ 
(1 + z^4 + 2*z^2)/(24*z^4 + 24*z^6 + 52*z^2)
Trigonometric part [src] 
                2         
        /     2\          
        \1 + z /          
--------------------------
     /           /     2\\
   2 |         2 |1   z ||
4*z *|13 + 12*z *|- + --||
     \           \2   2 //
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(12 z^{2} \left(\frac{z^{2}}{2} + \frac{1}{2}\right) + 13\right)}$$ 
(1 + z^2)^2/(4*z^2*(13 + 12*z^2*(1/2 + z^2/2)))
Powers [src] 
                2         
        /     2\          
        \1 + z /          
--------------------------
     /           /     2\\
   2 |         2 |1   z ||
4*z *|13 + 12*z *|- + --||
     \           \2   2 //
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(12 z^{2} \left(\frac{z^{2}}{2} + \frac{1}{2}\right) + 13\right)}$$ 
                2        
        /     2\         
        \1 + z /         
-------------------------
   2 /      2 /       2\\
4*z *\13 + z *\6 + 6*z //
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(z^{2} \left(6 z^{2} + 6\right) + 13\right)}$$ 
(1 + z^2)^2/(4*z^2*(13 + z^2*(6 + 6*z^2)))
Combinatorics [src] 
               2       
       /     2\        
       \1 + z /        
-----------------------
   2 /        2      4\
4*z *\13 + 6*z  + 6*z /
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(6 z^{4} + 6 z^{2} + 13\right)}$$ 
(1 + z^2)^2/(4*z^2*(13 + 6*z^2 + 6*z^4))
Combining rational expressions [src] 
                2        
        /     2\         
        \1 + z /         
-------------------------
   2 /        2 /     2\\
4*z *\13 + 6*z *\1 + z //
$$\frac{\left(z^{2} + 1\right)^{2}}{4 z^{2} \left(6 z^{2} \left(z^{2} + 1\right) + 13\right)}$$ 
(1 + z^2)^2/(4*z^2*(13 + 6*z^2*(1 + z^2)))
Numerical answer [src] 
0.25*(1.0 + z^2)^2/(z^2*(13.0 + 6.0*z^2*(1.0 + z^2)))
0.25*(1.0 + z^2)^2/(z^2*(13.0 + 6.0*z^2*(1.0 + z^2)))
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