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Expression simplification/ Fraction Decomposition into the simple/ ((z^2-z)/(z^2-9))^-1/(z^2-3*z)/(z-1)

How do you ((z^2-z)/(z^2-9))^-1/(z^2-3*z)/(z-1) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
/        1        \
|-----------------|
| 2               |
|z  - z / 2      \|
|------*\z  - 3*z/|
| 2               |
\z  - 9           /
-------------------
       z - 1
$$\frac{\frac{1}{\frac{1}{z^{2} - 9} \left(z^{2} - z\right)} \frac{1}{z^{2} - 3 z}}{z - 1}$$ 
(1/((((z^2 - z)/(z^2 - 9)))*(z^2 - 3*z)))/(z - 1)
Fraction decomposition [src] 
-7/(-1 + z) + 3/z^2 + 4/(-1 + z)^2 + 7/z
$$- \frac{7}{z - 1} + \frac{4}{\left(z - 1\right)^{2}} + \frac{7}{z} + \frac{3}{z^{2}}$$ 
    7      3        4       7
- ------ + -- + --------- + -
  -1 + z    2           2   z
           z    (-1 + z)
General simplification [src] 
      3 + z      
-----------------
 2 /     2      \
z *\1 + z  - 2*z/
$$\frac{z + 3}{z^{2} \left(z^{2} - 2 z + 1\right)}$$ 
(3 + z)/(z^2*(1 + z^2 - 2*z))
Trigonometric part [src] 
                2           
          -9 + z            
----------------------------
         / 2    \ / 2      \
(-1 + z)*\z  - z/*\z  - 3*z/
$$\frac{z^{2} - 9}{\left(z - 1\right) \left(z^{2} - 3 z\right) \left(z^{2} - z\right)}$$ 
(-9 + z^2)/((-1 + z)*(z^2 - z)*(z^2 - 3*z))
Assemble expression [src] 
                2           
          -9 + z            
----------------------------
         / 2    \ / 2      \
(-1 + z)*\z  - z/*\z  - 3*z/
$$\frac{z^{2} - 9}{\left(z - 1\right) \left(z^{2} - 3 z\right) \left(z^{2} - z\right)}$$ 
(-9 + z^2)/((-1 + z)*(z^2 - z)*(z^2 - 3*z))
Rational denominator [src] 
                2           
          -9 + z            
----------------------------
         / 2    \ / 2      \
(-1 + z)*\z  - z/*\z  - 3*z/
$$\frac{z^{2} - 9}{\left(z - 1\right) \left(z^{2} - 3 z\right) \left(z^{2} - z\right)}$$ 
(-9 + z^2)/((-1 + z)*(z^2 - z)*(z^2 - 3*z))
Expand expression [src] 
            2              
           z  - 9          
---------------------------
        / 2    \ / 2      \
(z - 1)*\z  - z/*\z  - 3*z/
$$\frac{z^{2} - 9}{\left(z - 1\right) \left(z^{2} - 3 z\right) \left(z^{2} - z\right)}$$ 
(z^2 - 9)/((z - 1)*(z^2 - z)*(z^2 - 3*z))
Common denominator [src] 
    3 + z     
--------------
 2    4      3
z  + z  - 2*z
$$\frac{z + 3}{z^{4} - 2 z^{3} + z^{2}}$$ 
(3 + z)/(z^2 + z^4 - 2*z^3)
Combinatorics [src] 
   3 + z    
------------
 2         2
z *(-1 + z)
$$\frac{z + 3}{z^{2} \left(z - 1\right)^{2}}$$ 
(3 + z)/(z^2*(-1 + z)^2)
Combining rational expressions [src] 
             2       
       -9 + z        
---------------------
 2         2         
z *(-1 + z) *(-3 + z)
$$\frac{z^{2} - 9}{z^{2} \left(z - 3\right) \left(z - 1\right)^{2}}$$ 
(-9 + z^2)/(z^2*(-1 + z)^2*(-3 + z))
Powers [src] 
                2           
          -9 + z            
----------------------------
         / 2    \ / 2      \
(-1 + z)*\z  - z/*\z  - 3*z/
$$\frac{z^{2} - 9}{\left(z - 1\right) \left(z^{2} - 3 z\right) \left(z^{2} - z\right)}$$ 
(-9 + z^2)/((-1 + z)*(z^2 - z)*(z^2 - 3*z))
Numerical answer [src] 
(-9.0 + z^2)/((-1.0 + z)*(z^2 - z)*(z^2 - 3.0*z))
(-9.0 + z^2)/((-1.0 + z)*(z^2 - z)*(z^2 - 3.0*z))
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