1/(x-1)=(x-1)/x

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


D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:0) U (0:1) U (1:+oo)

1/(x-1) = (x-1)/x // - (x-1)/x

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

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

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

1*x-1*(x-1)^2 = 0

3*x-x^2-1 = 0

3*x-x^2-1 = 0

3*x-x^2-1 = 0

DELTA = 3^2-(-1*(-1)*4)

DELTA = 5

DELTA > 0

x = (5^(1/2)-3)/(-1*2) or x = (-5^(1/2)-3)/(-1*2)

x = (5^(1/2)-3)/(-2) or x = (5^(1/2)+3)/2

(x-((5^(1/2)-3)/(-2)))*(x-((5^(1/2)+3)/2)) = 0

((x-((5^(1/2)-3)/(-2)))*(x-((5^(1/2)+3)/2)))/(x*(x-1)) = 0

((x-((5^(1/2)-3)/(-2)))*(x-((5^(1/2)+3)/2)))/(x*(x-1)) = 0 // * x*(x-1)

(x-((5^(1/2)-3)/(-2)))*(x-((5^(1/2)+3)/2)) = 0

( x-((5^(1/2)+3)/2) )

x-((5^(1/2)+3)/2) = 0 // + (5^(1/2)+3)/2

x = (5^(1/2)+3)/2

( x-((5^(1/2)-3)/(-2)) )

x-((5^(1/2)-3)/(-2)) = 0 // + (5^(1/2)-3)/(-2)

x = (5^(1/2)-3)/(-2)

x in { (5^(1/2)+3)/2, (5^(1/2)-3)/(-2) }

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