2x/(x-2)=5+(13x^2)/(x-2)

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Solution for 2x/(x-2)=5+(13x^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) = (13*x^2)/(x-2)+5 // - (13*x^2)/(x-2)+5

(2*x)/(x-2)-((13*x^2)/(x-2))-5 = 0

(2*x)/(x-2)-13*x^2*(x-2)^-1-5 = 0

(2*x)/(x-2)+(-13*x^2)/(x-2)-5 = 0

(2*x)/(x-2)+(-13*x^2)/(x-2)+(-5*(x-2))/(x-2) = 0

2*x-5*(x-2)-13*x^2 = 0

2*x-13*x^2-5*x+10 = 0

10-13*x^2-3*x = 0

10-13*x^2-3*x = 0

10-13*x^2-3*x = 0

DELTA = (-3)^2-(-13*4*10)

DELTA = 529

DELTA > 0

x = (529^(1/2)+3)/(-13*2) or x = (3-529^(1/2))/(-13*2)

x = -1 or x = 10/13

(x+1)*(x-10/13) = 0

((x+1)*(x-10/13))/(x-2) = 0

((x+1)*(x-10/13))/(x-2) = 0 // * x-2

(x+1)*(x-10/13) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-10/13 )

x-10/13 = 0 // + 10/13

x = 10/13

x in { -1, 10/13 }

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