Fraction decomposition
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-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
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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)
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)
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
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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)
/ 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
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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)
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)
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
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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)