(1/x)+(1/(x-1))=1/4

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Solution for (1/x)+(1/(x-1))=1/4 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)+1/x = 1/4 // - 1/4

1/(x-1)+1/x-(1/4) = 0

1/(x-1)+1/x-1/4 = 0

(1*4*x)/(4*x*(x-1))+(1*4*(x-1))/(4*x*(x-1))+(-1*x*(x-1))/(4*x*(x-1)) = 0

1*4*(x-1)-1*x*(x-1)+1*4*x = 0

8*x-x^2+x-4 = 0

9*x-x^2-4 = 0

9*x-x^2-4 = 0

9*x-x^2-4 = 0

DELTA = 9^2-(-4*(-1)*4)

DELTA = 65

DELTA > 0

x = (65^(1/2)-9)/(-1*2) or x = (-65^(1/2)-9)/(-1*2)

x = (65^(1/2)-9)/(-2) or x = (65^(1/2)+9)/2

(x-((65^(1/2)-9)/(-2)))*(x-((65^(1/2)+9)/2)) = 0

((x-((65^(1/2)-9)/(-2)))*(x-((65^(1/2)+9)/2)))/(4*x*(x-1)) = 0

((x-((65^(1/2)-9)/(-2)))*(x-((65^(1/2)+9)/2)))/(4*x*(x-1)) = 0 // * 4*x*(x-1)

(x-((65^(1/2)-9)/(-2)))*(x-((65^(1/2)+9)/2)) = 0

( x-((65^(1/2)+9)/2) )

x-((65^(1/2)+9)/2) = 0 // + (65^(1/2)+9)/2

x = (65^(1/2)+9)/2

( x-((65^(1/2)-9)/(-2)) )

x-((65^(1/2)-9)/(-2)) = 0 // + (65^(1/2)-9)/(-2)

x = (65^(1/2)-9)/(-2)

x in { (65^(1/2)+9)/2, (65^(1/2)-9)/(-2) }

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