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Expression simplification/ Fraction Decomposition into the simple/ ((9n)/(5m))-((81n^2+25m^2)/(45mn))+((5m-9n)/(9n))

How do you ((9n)/(5m))-((81n^2+25m^2)/(45mn))+((5m-9n)/(9n)) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
          2       2            
9*n   81*n  + 25*m    5*m - 9*n
--- - ------------- + ---------
5*m       45*m*n         9*n
$$\left(- \frac{25 m^{2} + 81 n^{2}}{45 m n} + \frac{9 n}{5 m}\right) + \frac{5 m - 9 n}{9 n}$$ 
(9*n)/((5*m)) - (81*n^2 + 25*m^2)/((45*m)*n) + (5*m - 9*n)/((9*n))
Fraction decomposition [src] 
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General simplification [src] 
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Numerical answer [src] 
0.111111111111111*(5.0*m - 9.0*n)/n + 1.8*n/m - 0.0222222222222222*(25.0*m^2 + 81.0*n^2)/(m*n)
0.111111111111111*(5.0*m - 9.0*n)/n + 1.8*n/m - 0.0222222222222222*(25.0*m^2 + 81.0*n^2)/(m*n)
Trigonometric part [src] 
                       2       2
-9*n + 5*m   9*n   25*m  + 81*n 
---------- + --- - -------------
   9*n       5*m       45*m*n
$$\frac{5 m - 9 n}{9 n} + \frac{9 n}{5 m} - \frac{25 m^{2} + 81 n^{2}}{45 m n}$$ 
(-9*n + 5*m)/(9*n) + 9*n/(5*m) - (25*m^2 + 81*n^2)/(45*m*n)
Expand expression [src] 
                      2       2
5*m - 9*n   9*n   81*n  + 25*m 
--------- + --- - -------------
   9*n      5*m       45*m*n
$$\frac{5 m - 9 n}{9 n} + \frac{9 n}{5 m} - \frac{25 m^{2} + 81 n^{2}}{45 m n}$$ 
(5*m - 9*n)/(9*n) + 9*n/(5*m) - (81*n^2 + 25*m^2)/(45*m*n)
Common denominator [src] 
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Combinatorics [src] 
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Assemble expression [src] 
          2       2             
9*n   25*m  + 81*n              
--- - -------------             
 5         45*n       -9*n + 5*m
------------------- + ----------
         m               9*n
$$\frac{5 m - 9 n}{9 n} + \frac{\frac{9 n}{5} - \frac{25 m^{2} + 81 n^{2}}{45 n}}{m}$$ 
                       2       2
-9*n + 5*m   9*n   25*m  + 81*n 
---------- + --- - -------------
   9*n       5*m       45*m*n
$$\frac{5 m - 9 n}{9 n} + \frac{9 n}{5 m} - \frac{25 m^{2} + 81 n^{2}}{45 m n}$$ 
               2       2      
     5*m   25*m  + 81*n       
-n + --- - -------------      
      9         45*m       9*n
------------------------ + ---
           n               5*m
$$\frac{\frac{5 m}{9} - n - \frac{25 m^{2} + 81 n^{2}}{45 m}}{n} + \frac{9 n}{5 m}$$ 
(-n + 5*m/9 - (25*m^2 + 81*n^2)/(45*m))/n + 9*n/(5*m)
Combining rational expressions [src] 
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Powers [src] 
                       2       2
-9*n + 5*m   9*n   25*m  + 81*n 
---------- + --- - -------------
   9*n       5*m       45*m*n
$$\frac{5 m - 9 n}{9 n} + \frac{9 n}{5 m} - \frac{25 m^{2} + 81 n^{2}}{45 m n}$$ 
                      2      2
     5*m           9*n    5*m 
-n + ---         - ---- - ----
      9    9*n      5      9  
-------- + --- + -------------
   n       5*m        m*n
$$\frac{\frac{5 m}{9} - n}{n} + \frac{9 n}{5 m} + \frac{- \frac{5 m^{2}}{9} - \frac{9 n^{2}}{5}}{m n}$$ 
(-n + 5*m/9)/n + 9*n/(5*m) + (-9*n^2/5 - 5*m^2/9)/(m*n)
Rational denominator [src] 
    /    /      2       2\          2\          2             
9*n*\5*m*\- 81*n  - 25*m / + 405*m*n / + 225*n*m *(-9*n + 5*m)
--------------------------------------------------------------
                                2  2                          
                          2025*m *n
$$\frac{225 m^{2} n \left(5 m - 9 n\right) + 9 n \left(405 m n^{2} + 5 m \left(- 25 m^{2} - 81 n^{2}\right)\right)}{2025 m^{2} n^{2}}$$ 
(9*n*(5*m*(-81*n^2 - 25*m^2) + 405*m*n^2) + 225*n*m^2*(-9*n + 5*m))/(2025*m^2*n^2)
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