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

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Solution for (4x+1)/(x-2)+2/x=-4/(x^2-2x) equation: 


D( x )

x^2-(2*x) = 0

x-2 = 0

x = 0

x^2-(2*x) = 0

x^2-(2*x) = 0

x^2-2*x = 0

x^2-2*x = 0

DELTA = (-2)^2-(0*1*4)

DELTA = 4

DELTA > 0

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

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

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

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

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

x^2-2*x = 0

x^2-2*x = 0

x*(x-2) = 0

x-2 = 0 // + 2

x = 2

x*(x-2) = 0

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

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

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

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

4*x^2+3*x = 0

4*x^2+3*x = 0

x*(4*x+3) = 0

4*x+3 = 0 // - 3

4*x = -3 // : 4

x = -3/4

x*(x+3/4) = 0

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

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

x*(x+3/4) = 0

( x+3/4 )

x+3/4 = 0 // - 3/4

x = -3/4

( x )

x = 0

x in { 0} 

x = -3/4

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