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

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

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

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

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

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

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

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

DELTA = 2^2-(-2*4*5)

DELTA = 44

DELTA > 0

x = (44^(1/2)-2)/(2*5) or x = (-44^(1/2)-2)/(2*5)

x = (2*11^(1/2)-2)/10 or x = (-2*11^(1/2)-2)/10

(x-((-2*11^(1/2)-2)/10))*(x-((2*11^(1/2)-2)/10)) = 0

((x-((-2*11^(1/2)-2)/10))*(x-((2*11^(1/2)-2)/10)))/(x*(x-1)) = 0

((x-((-2*11^(1/2)-2)/10))*(x-((2*11^(1/2)-2)/10)))/(x*(x-1)) = 0 // * x*(x-1)

(x-((-2*11^(1/2)-2)/10))*(x-((2*11^(1/2)-2)/10)) = 0

( x-((-2*11^(1/2)-2)/10) )

x-((-2*11^(1/2)-2)/10) = 0 // + (-2*11^(1/2)-2)/10

x = (-2*11^(1/2)-2)/10

( x-((2*11^(1/2)-2)/10) )

x-((2*11^(1/2)-2)/10) = 0 // + (2*11^(1/2)-2)/10

x = (2*11^(1/2)-2)/10

x in { (-2*11^(1/2)-2)/10, (2*11^(1/2)-2)/10 }

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