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Expression simplification/ Fraction Decomposition into the simple/ (5*a^2+3*a-2)/(a^2-1)

How do you (5*a^2+3*a-2)/(a^2-1) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
   2          
5*a  + 3*a - 2
--------------
     2        
    a  - 1
$$\frac{\left(5 a^{2} + 3 a\right) - 2}{a^{2} - 1}$$ 
(5*a^2 + 3*a - 2)/(a^2 - 1)
Fraction decomposition [src] 
5 + 3/(-1 + a)
$$5 + \frac{3}{a - 1}$$ 
      3   
5 + ------
    -1 + a
General simplification [src] 
-2 + 5*a
--------
 -1 + a
$$\frac{5 a - 2}{a - 1}$$ 
(-2 + 5*a)/(-1 + a)
Trigonometric part [src] 
              2
-2 + 3*a + 5*a 
---------------
          2    
    -1 + a
$$\frac{5 a^{2} + 3 a - 2}{a^{2} - 1}$$ 
(-2 + 3*a + 5*a^2)/(-1 + a^2)
Powers [src] 
              2
-2 + 3*a + 5*a 
---------------
          2    
    -1 + a
$$\frac{5 a^{2} + 3 a - 2}{a^{2} - 1}$$ 
(-2 + 3*a + 5*a^2)/(-1 + a^2)
Assemble expression [src] 
              2
-2 + 3*a + 5*a 
---------------
          2    
    -1 + a
$$\frac{5 a^{2} + 3 a - 2}{a^{2} - 1}$$ 
(-2 + 3*a + 5*a^2)/(-1 + a^2)
Combinatorics [src] 
-2 + 5*a
--------
 -1 + a
$$\frac{5 a - 2}{a - 1}$$ 
(-2 + 5*a)/(-1 + a)
Common denominator [src] 
      3   
5 + ------
    -1 + a
$$5 + \frac{3}{a - 1}$$ 
5 + 3/(-1 + a)
Rational denominator [src] 
              2
-2 + 3*a + 5*a 
---------------
          2    
    -1 + a
$$\frac{5 a^{2} + 3 a - 2}{a^{2} - 1}$$ 
(-2 + 3*a + 5*a^2)/(-1 + a^2)
Numerical answer [src] 
(-2.0 + 3.0*a + 5.0*a^2)/(-1.0 + a^2)
(-2.0 + 3.0*a + 5.0*a^2)/(-1.0 + a^2)
Combining rational expressions [src] 
-2 + a*(3 + 5*a)
----------------
          2     
    -1 + a
$$\frac{a \left(5 a + 3\right) - 2}{a^{2} - 1}$$ 
(-2 + a*(3 + 5*a))/(-1 + a^2)
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