(6x)/(x-6)=9+(2x^2)/(x-6)

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Solution for (6x)/(x-6)=9+(2x^2)/(x-6) equation: 


D( x )

x-6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x in (-oo:6) U (6:+oo)

(6*x)/(x-6) = (2*x^2)/(x-6)+9 // - (2*x^2)/(x-6)+9

(6*x)/(x-6)-((2*x^2)/(x-6))-9 = 0

(6*x)/(x-6)-2*x^2*(x-6)^-1-9 = 0

(6*x)/(x-6)+(-2*x^2)/(x-6)-9 = 0

(6*x)/(x-6)+(-2*x^2)/(x-6)+(-9*(x-6))/(x-6) = 0

6*x-9*(x-6)-2*x^2 = 0

6*x-2*x^2-9*x+54 = 0

54-2*x^2-3*x = 0

54-2*x^2-3*x = 0

54-2*x^2-3*x = 0

DELTA = (-3)^2-(-2*4*54)

DELTA = 441

DELTA > 0

x = (441^(1/2)+3)/(-2*2) or x = (3-441^(1/2))/(-2*2)

x = -6 or x = 9/2

(x+6)*(x-9/2) = 0

((x+6)*(x-9/2))/(x-6) = 0

((x+6)*(x-9/2))/(x-6) = 0 // * x-6

(x+6)*(x-9/2) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-9/2 )

x-9/2 = 0 // + 9/2

x = 9/2

x in { -6, 9/2 }

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