6-(2/x)=4/(x-1)

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Solution for 6-(2/x)=4/(x-1) 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)

6-(2/x) = 4/(x-1) // - 4/(x-1)

6-(4/(x-1))-(2/x) = 0

6-4*(x-1)^-1-2*x^-1 = 0

6-4/(x-1)-2/x = 0

(-4*x)/(x*(x-1))+(-2*(x-1))/(x*(x-1))+(6*x*(x-1))/(x*(x-1)) = 0

6*x*(x-1)-2*(x-1)-4*x = 0

6*x^2-6*x-6*x+2 = 0

6*x^2-12*x+2 = 0

6*x^2-12*x+2 = 0

2*(3*x^2-6*x+1) = 0

3*x^2-6*x+1 = 0

DELTA = (-6)^2-(1*3*4)

DELTA = 24

DELTA > 0

x = (24^(1/2)+6)/(2*3) or x = (6-24^(1/2))/(2*3)

x = (2*6^(1/2)+6)/6 or x = (6-2*6^(1/2))/6

2*(x-((6-2*6^(1/2))/6))*(x-((2*6^(1/2)+6)/6)) = 0

(2*(x-((6-2*6^(1/2))/6))*(x-((2*6^(1/2)+6)/6)))/(x*(x-1)) = 0

(2*(x-((6-2*6^(1/2))/6))*(x-((2*6^(1/2)+6)/6)))/(x*(x-1)) = 0 // * x*(x-1)

2*(x-((6-2*6^(1/2))/6))*(x-((2*6^(1/2)+6)/6)) = 0

( x-((2*6^(1/2)+6)/6) )

x-((2*6^(1/2)+6)/6) = 0 // + (2*6^(1/2)+6)/6

x = (2*6^(1/2)+6)/6

( x-((6-2*6^(1/2))/6) )

x-((6-2*6^(1/2))/6) = 0 // + (6-2*6^(1/2))/6

x = (6-2*6^(1/2))/6

x in { (2*6^(1/2)+6)/6, (6-2*6^(1/2))/6 }

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