prove that ((2x^3 −x^2 −2x+1)/(x^3 +1)) + ((x^3 +1)/(x^4 −2x^3 +3x^2 −2x+1)) = 2


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Question Number 69662 by aliesam last updated on 26/Sep/19

$p r o v e t h a t$ $\frac{2 x^{3} - x^{2} - 2 x + 1}{x^{3} + 1} + \frac{x^{3} + 1}{x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1} = 2$
	Answered by MJS last updated on 26/Sep/19

	$\frac{(x - 1) (2 x - 1) (x + 1)}{(x + 1) (x^{2} - x + 1)} + \frac{(x + 1) (x^{2} - x + 1)}{{(x^{2} - x + 1)}^{2}} =$ $= \frac{(x - 1) (2 x - 1) + (x + 1)}{x^{2} - x + 1} = \frac{2 x^{2} - 2 x + 2}{x^{2} - x + 1} = 2$
	Commented by aliesam last updated on 26/Sep/19

	$t h a n k y o u s i r$
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