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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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