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Expression simplification/ Fraction Decomposition into the simple/ ((25*x^2)-1)/((25*x^2)-10*x+1)

How do you ((25*x^2)-1)/((25*x^2)-10*x+1) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
       2        
   25*x  - 1    
----------------
    2           
25*x  - 10*x + 1
$$\frac{25 x^{2} - 1}{\left(25 x^{2} - 10 x\right) + 1}$$ 
(25*x^2 - 1)/(25*x^2 - 10*x + 1)
General simplification [src] 
1 + 5*x 
--------
-1 + 5*x
$$\frac{5 x + 1}{5 x - 1}$$ 
(1 + 5*x)/(-1 + 5*x)
Fraction decomposition [src] 
1 + 2/(-1 + 5*x)
$$1 + \frac{2}{5 x - 1}$$ 
       2    
1 + --------
    -1 + 5*x
Trigonometric part [src] 
            2   
   -1 + 25*x    
----------------
               2
1 - 10*x + 25*x
$$\frac{25 x^{2} - 1}{25 x^{2} - 10 x + 1}$$ 
(-1 + 25*x^2)/(1 - 10*x + 25*x^2)
Rational denominator [src] 
            2   
   -1 + 25*x    
----------------
               2
1 - 10*x + 25*x
$$\frac{25 x^{2} - 1}{25 x^{2} - 10 x + 1}$$ 
(-1 + 25*x^2)/(1 - 10*x + 25*x^2)
Common denominator [src] 
       2    
1 + --------
    -1 + 5*x
$$1 + \frac{2}{5 x - 1}$$ 
1 + 2/(-1 + 5*x)
Combinatorics [src] 
1 + 5*x 
--------
-1 + 5*x
$$\frac{5 x + 1}{5 x - 1}$$ 
(1 + 5*x)/(-1 + 5*x)
Combining rational expressions [src] 
             2    
    -1 + 25*x     
------------------
1 + 5*x*(-2 + 5*x)
$$\frac{25 x^{2} - 1}{5 x \left(5 x - 2\right) + 1}$$ 
(-1 + 25*x^2)/(1 + 5*x*(-2 + 5*x))
Powers [src] 
            2   
   -1 + 25*x    
----------------
               2
1 - 10*x + 25*x
$$\frac{25 x^{2} - 1}{25 x^{2} - 10 x + 1}$$ 
(-1 + 25*x^2)/(1 - 10*x + 25*x^2)
Numerical answer [src] 
(-1.0 + 25.0*x^2)/(1.0 + 25.0*x^2 - 10.0*x)
(-1.0 + 25.0*x^2)/(1.0 + 25.0*x^2 - 10.0*x)
Assemble expression [src] 
            2   
   -1 + 25*x    
----------------
               2
1 - 10*x + 25*x
$$\frac{25 x^{2} - 1}{25 x^{2} - 10 x + 1}$$ 
(-1 + 25*x^2)/(1 - 10*x + 25*x^2)
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