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Expression simplification/ Fraction Decomposition into the simple/ ((x+12)/(x^(3)-9x))/(((x-3)/(2x^2+5x-3))-(9/(9-x^2)))

How do you ((x+12)/(x^(3)-9x))/(((x-3)/(2x^2+5x-3))-(9/(9-x^2))) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
       / x + 12 \      
       |--------|      
       | 3      |      
       \x  - 9*x/      
-----------------------
    x - 3          9   
-------------- - ------
   2                  2
2*x  + 5*x - 3   9 - x
$$\frac{\left(x + 12\right) \frac{1}{x^{3} - 9 x}}{\frac{x - 3}{\left(2 x^{2} + 5 x\right) - 3} - \frac{9}{9 - x^{2}}}$$ 
((x + 12)/(x^3 - 9*x))/((x - 3)/(2*x^2 + 5*x - 3) - 9/(9 - x^2))
General simplification [src] 
-1 + 2*x
--------
    2   
   x
$$\frac{2 x - 1}{x^{2}}$$ 
(-1 + 2*x)/x^2
Fraction decomposition [src] 
-1/x^2 + 2/x
$$\frac{2}{x} - \frac{1}{x^{2}}$$ 
  1    2
- -- + -
   2   x
  x
Numerical answer [src] 
(12.0 + x)/((x^3 - 9.0*x)*(-9.0/(9.0 - x^2) + (-3.0 + x)/(-3.0 + 2.0*x^2 + 5.0*x)))
(12.0 + x)/((x^3 - 9.0*x)*(-9.0/(9.0 - x^2) + (-3.0 + x)/(-3.0 + 2.0*x^2 + 5.0*x)))
Rational denominator [src] 
                   2      5       4       3
324 - 513*x - 297*x  + 2*x  + 29*x  + 39*x 
-------------------------------------------
       / 3      \ / 3       2       \      
       \x  - 9*x/*\x  + 15*x  + 36*x/
$$\frac{2 x^{5} + 29 x^{4} + 39 x^{3} - 297 x^{2} - 513 x + 324}{\left(x^{3} - 9 x\right) \left(x^{3} + 15 x^{2} + 36 x\right)}$$ 
(324 - 513*x - 297*x^2 + 2*x^5 + 29*x^4 + 39*x^3)/((x^3 - 9*x)*(x^3 + 15*x^2 + 36*x))
Powers [src] 
                 12 + x                
---------------------------------------
/ 3      \ /    9           -3 + x    \
\x  - 9*x/*|- ------ + ---------------|
           |       2           2      |
           \  9 - x    -3 + 2*x  + 5*x/
$$\frac{x + 12}{\left(x^{3} - 9 x\right) \left(\frac{x - 3}{2 x^{2} + 5 x - 3} - \frac{9}{9 - x^{2}}\right)}$$ 
(12 + x)/((x^3 - 9*x)*(-9/(9 - x^2) + (-3 + x)/(-3 + 2*x^2 + 5*x)))
Assemble expression [src] 
                 12 + x                
---------------------------------------
/ 3      \ /    9           -3 + x    \
\x  - 9*x/*|- ------ + ---------------|
           |       2           2      |
           \  9 - x    -3 + 2*x  + 5*x/
$$\frac{x + 12}{\left(x^{3} - 9 x\right) \left(\frac{x - 3}{2 x^{2} + 5 x - 3} - \frac{9}{9 - x^{2}}\right)}$$ 
(12 + x)/((x^3 - 9*x)*(-9/(9 - x^2) + (-3 + x)/(-3 + 2*x^2 + 5*x)))
Trigonometric part [src] 
                 12 + x                
---------------------------------------
/ 3      \ /    9           -3 + x    \
\x  - 9*x/*|- ------ + ---------------|
           |       2           2      |
           \  9 - x    -3 + 2*x  + 5*x/
$$\frac{x + 12}{\left(x^{3} - 9 x\right) \left(\frac{x - 3}{2 x^{2} + 5 x - 3} - \frac{9}{9 - x^{2}}\right)}$$ 
(12 + x)/((x^3 - 9*x)*(-9/(9 - x^2) + (-3 + x)/(-3 + 2*x^2 + 5*x)))
Common denominator [src] 
-1 + 2*x
--------
    2   
   x
$$\frac{2 x - 1}{x^{2}}$$ 
(-1 + 2*x)/x^2
Combinatorics [src] 
-1 + 2*x
--------
    2   
   x
$$\frac{2 x - 1}{x^{2}}$$ 
(-1 + 2*x)/x^2
Combining rational expressions [src] 
                           /     2\                 
        (-3 + x*(5 + 2*x))*\9 - x /*(12 + x)        
----------------------------------------------------
  /      2\ /              /     2\                \
x*\-9 + x /*\27 + (-3 + x)*\9 - x / - 9*x*(5 + 2*x)/
$$\frac{\left(9 - x^{2}\right) \left(x + 12\right) \left(x \left(2 x + 5\right) - 3\right)}{x \left(x^{2} - 9\right) \left(- 9 x \left(2 x + 5\right) + \left(9 - x^{2}\right) \left(x - 3\right) + 27\right)}$$ 
(-3 + x*(5 + 2*x))*(9 - x^2)*(12 + x)/(x*(-9 + x^2)*(27 + (-3 + x)*(9 - x^2) - 9*x*(5 + 2*x)))
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