Mister Exam

# How do you 6/(c-1)-10/(((c-1)^2)*10*(c^2))-1-2*c+2/c-1 in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
  6           10                   2
----- - -------------- - 1 - 2*c + - - 1
c - 1          2     2             c
(c - 1) *10*c                   
$$\left(\left(- 2 c + \left(\left(\frac{6}{c - 1} - \frac{10}{c^{2} \cdot 10 \left(c - 1\right)^{2}}\right) - 1\right)\right) + \frac{2}{c}\right) - 1$$
6/(c - 1) - 10*1/(10*c^2*(c - 1)^2) - 1 - 2*c + 2/c - 1
Fraction decomposition [src]
-2 - 1/c^2 - 1/(-1 + c)^2 - 2*c + 8/(-1 + c)
$$- 2 c - 2 + \frac{8}{c - 1} - \frac{1}{\left(c - 1\right)^{2}} - \frac{1}{c^{2}}$$
     1        1               8
-2 - -- - --------- - 2*c + ------
2           2         -1 + c
c    (-1 + c)                
General simplification [src]
         2      5            4       3
-1 - 12*c  - 2*c  + 2*c + 2*c  + 10*c
--------------------------------------
2 /     2      \
c *\1 + c  - 2*c/           
$$\frac{- 2 c^{5} + 2 c^{4} + 10 c^{3} - 12 c^{2} + 2 c - 1}{c^{2} \left(c^{2} - 2 c + 1\right)}$$
(-1 - 12*c^2 - 2*c^5 + 2*c + 2*c^4 + 10*c^3)/(c^2*(1 + c^2 - 2*c))
-2.0 + 2.0/c + 6.0/(-1.0 + c) - 2.0*c - 1.0/(c^2*(-1.0 + c)^2)
-2.0 + 2.0/c + 6.0/(-1.0 + c) - 2.0*c - 1.0/(c^2*(-1.0 + c)^2)
Common denominator [src]
                    2            3
-1 - 10*c  + 2*c + 8*c
-2 - 2*c + -----------------------
2    4      3
c  + c  - 2*c     
$$- 2 c - 2 + \frac{8 c^{3} - 10 c^{2} + 2 c - 1}{c^{4} - 2 c^{3} + c^{2}}$$
-2 - 2*c + (-1 - 10*c^2 + 2*c + 8*c^3)/(c^2 + c^4 - 2*c^3)
Powers [src]
           2     6           1
-2 - 2*c + - + ------ - ------------
c   -1 + c    2         2
c *(-1 + c) 
$$- 2 c - 2 + \frac{6}{c - 1} + \frac{2}{c} - \frac{1}{c^{2} \left(c - 1\right)^{2}}$$
-2 - 2*c + 2/c + 6/(-1 + c) - 1/(c^2*(-1 + c)^2)
Assemble expression [src]
           2     6           1
-2 - 2*c + - + ------ - ------------
c   -1 + c    2         2
c *(-1 + c) 
$$- 2 c - 2 + \frac{6}{c - 1} + \frac{2}{c} - \frac{1}{c^{2} \left(c - 1\right)^{2}}$$
-2 - 2*c + 2/c + 6/(-1 + c) - 1/(c^2*(-1 + c)^2)
Combinatorics [src]
 /        3            4      5       2\
-\1 - 10*c  - 2*c - 2*c  + 2*c  + 12*c /
-----------------------------------------
2         2
c *(-1 + c)               
$$- \frac{2 c^{5} - 2 c^{4} - 10 c^{3} + 12 c^{2} - 2 c + 1}{c^{2} \left(c - 1\right)^{2}}$$
-(1 - 10*c^3 - 2*c - 2*c^4 + 2*c^5 + 12*c^2)/(c^2*(-1 + c)^2)
Combining rational expressions [src]
        2         2      3         2               2      2
-1 - 2*c *(-1 + c)  - 2*c *(-1 + c)  + 2*c*(-1 + c)  + 6*c *(-1 + c)
--------------------------------------------------------------------
2         2
c *(-1 + c)                             
$$\frac{- 2 c^{3} \left(c - 1\right)^{2} - 2 c^{2} \left(c - 1\right)^{2} + 6 c^{2} \left(c - 1\right) + 2 c \left(c - 1\right)^{2} - 1}{c^{2} \left(c - 1\right)^{2}}$$
(-1 - 2*c^2*(-1 + c)^2 - 2*c^3*(-1 + c)^2 + 2*c*(-1 + c)^2 + 6*c^2*(-1 + c))/(c^2*(-1 + c)^2)
Expand expression [src]
           2     6          1
-2 - 2*c + - + ----- - -----------
c   c - 1    2        2
c *(c - 1) 
$$- 2 c - 2 + \frac{6}{c - 1} + \frac{2}{c} - \frac{1}{c^{2} \left(c - 1\right)^{2}}$$
-2 - 2*c + 2/c + 6/(c - 1) - 1/(c^2*(c - 1)^2)
Trigonometric part [src]
           2     6           1
-2 - 2*c + - + ------ - ------------
c   -1 + c    2         2
c *(-1 + c) 
$$- 2 c - 2 + \frac{6}{c - 1} + \frac{2}{c} - \frac{1}{c^{2} \left(c - 1\right)^{2}}$$
-2 - 2*c + 2/c + 6/(-1 + c) - 1/(c^2*(-1 + c)^2)
Rational denominator [src]
      2              3         3       4         3       2         3       3         2
- 10*c  + 10*c - 20*c *(-1 + c)  - 20*c *(-1 + c)  + 20*c *(-1 + c)  + 60*c *(-1 + c)
--------------------------------------------------------------------------------------
3         3
10*c *(-1 + c)                                     
$$\frac{- 20 c^{4} \left(c - 1\right)^{3} - 20 c^{3} \left(c - 1\right)^{3} + 60 c^{3} \left(c - 1\right)^{2} + 20 c^{2} \left(c - 1\right)^{3} - 10 c^{2} + 10 c}{10 c^{3} \left(c - 1\right)^{3}}$$
(-10*c^2 + 10*c - 20*c^3*(-1 + c)^3 - 20*c^4*(-1 + c)^3 + 20*c^2*(-1 + c)^3 + 60*c^3*(-1 + c)^2)/(10*c^3*(-1 + c)^3)
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