(6/x)-4/(x-2)+3

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Solution for (6/x)-4/(x-2)+3 equation: 


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

6/x-(4/(x-2))+3 = 0

6/x-4*(x-2)^-1+3 = 0

6/x-4/(x-2)+3 = 0

(-4*x)/(x*(x-2))+(6*(x-2))/(x*(x-2))+(3*x*(x-2))/(x*(x-2)) = 0

6*(x-2)+3*x*(x-2)-4*x = 0

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

3*x^2-4*x-12 = 0

3*x^2-4*x-12 = 0

3*x^2-4*x-12 = 0

DELTA = (-4)^2-(-12*3*4)

DELTA = 160

DELTA > 0

x = (160^(1/2)+4)/(2*3) or x = (4-160^(1/2))/(2*3)

x = (4*10^(1/2)+4)/6 or x = (4-4*10^(1/2))/6

(x-((4-4*10^(1/2))/6))*(x-((4*10^(1/2)+4)/6)) = 0

((x-((4-4*10^(1/2))/6))*(x-((4*10^(1/2)+4)/6)))/(x*(x-2)) = 0

((x-((4-4*10^(1/2))/6))*(x-((4*10^(1/2)+4)/6)))/(x*(x-2)) = 0 // * x*(x-2)

(x-((4-4*10^(1/2))/6))*(x-((4*10^(1/2)+4)/6)) = 0

( x-((4*10^(1/2)+4)/6) )

x-((4*10^(1/2)+4)/6) = 0 // + (4*10^(1/2)+4)/6

x = (4*10^(1/2)+4)/6

( x-((4-4*10^(1/2))/6) )

x-((4-4*10^(1/2))/6) = 0 // + (4-4*10^(1/2))/6

x = (4-4*10^(1/2))/6

x in { (4*10^(1/2)+4)/6, (4-4*10^(1/2))/6 }

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