4x/(x-2)+1/x=5

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Solution for 4x/(x-2)+1/x=5 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)

(4*x)/(x-2)+1/x = 5 // - 5

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

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

1*(x-2)-5*x*(x-2)+4*x*x = 0

4*x^2-5*x^2+x+10*x-2 = 0

11*x-x^2-2 = 0

11*x-x^2-2 = 0

11*x-x^2-2 = 0

DELTA = 11^2-(-2*(-1)*4)

DELTA = 113

DELTA > 0

x = (113^(1/2)-11)/(-1*2) or x = (-113^(1/2)-11)/(-1*2)

x = (113^(1/2)-11)/(-2) or x = (113^(1/2)+11)/2

(x-((113^(1/2)-11)/(-2)))*(x-((113^(1/2)+11)/2)) = 0

((x-((113^(1/2)-11)/(-2)))*(x-((113^(1/2)+11)/2)))/(x*(x-2)) = 0

((x-((113^(1/2)-11)/(-2)))*(x-((113^(1/2)+11)/2)))/(x*(x-2)) = 0 // * x*(x-2)

(x-((113^(1/2)-11)/(-2)))*(x-((113^(1/2)+11)/2)) = 0

( x-((113^(1/2)+11)/2) )

x-((113^(1/2)+11)/2) = 0 // + (113^(1/2)+11)/2

x = (113^(1/2)+11)/2

( x-((113^(1/2)-11)/(-2)) )

x-((113^(1/2)-11)/(-2)) = 0 // + (113^(1/2)-11)/(-2)

x = (113^(1/2)-11)/(-2)

x in { (113^(1/2)+11)/2, (113^(1/2)-11)/(-2) }

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