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

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Solution for (2x)/(x-2)=5+(4x^2)/(x-2) equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

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

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

(2*x)/(x-2)-((4*x^2)/(x-2))-5 = 0

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

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

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

2*x-5*(x-2)-4*x^2 = 0

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

10-4*x^2-3*x = 0

10-4*x^2-3*x = 0

10-4*x^2-3*x = 0

DELTA = (-3)^2-(-4*4*10)

DELTA = 169

DELTA > 0

x = (169^(1/2)+3)/(-4*2) or x = (3-169^(1/2))/(-4*2)

x = -2 or x = 5/4

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-5/4 )

x-5/4 = 0 // + 5/4

x = 5/4

x in { -2, 5/4 }

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