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

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

An expression to simplify:

The solution

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