x+((1)/(1-x))

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Solution for x+((1)/(1-x)) equation: 


D( x )

1-x = 0

1-x = 0

1-x = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

x in (-oo:1) U (1:+oo)

1/(1-x)+x = 0

1/(1-x)+(x*(1-x))/(1-x) = 0

x*(1-x)+1 = 0

x-x^2+1 = 0

x-x^2+1 = 0

x-x^2+1 = 0

DELTA = 1^2-(-1*1*4)

DELTA = 5

DELTA > 0

x = (5^(1/2)-1)/(-1*2) or x = (-5^(1/2)-1)/(-1*2)

x = (5^(1/2)-1)/(-2) or x = (5^(1/2)+1)/2

(x-((5^(1/2)-1)/(-2)))*(x-((5^(1/2)+1)/2)) = 0

((x-((5^(1/2)-1)/(-2)))*(x-((5^(1/2)+1)/2)))/(1-x) = 0

((x-((5^(1/2)-1)/(-2)))*(x-((5^(1/2)+1)/2)))/(1-x) = 0 // * 1-x

(x-((5^(1/2)-1)/(-2)))*(x-((5^(1/2)+1)/2)) = 0

( x-((5^(1/2)+1)/2) )

x-((5^(1/2)+1)/2) = 0 // + (5^(1/2)+1)/2

x = (5^(1/2)+1)/2

( x-((5^(1/2)-1)/(-2)) )

x-((5^(1/2)-1)/(-2)) = 0 // + (5^(1/2)-1)/(-2)

x = (5^(1/2)-1)/(-2)

x in { (5^(1/2)+1)/2, (5^(1/2)-1)/(-2) }

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