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D( x )
x-4 = 0
x-4 = 0
x-4 = 0
x-4 = 0 // + 4
x = 4
x in (-oo:4) U (4:+oo)
(4*x)/(x-4) = (10*x^2)/(x-4)+2 // - (10*x^2)/(x-4)+2
(4*x)/(x-4)-((10*x^2)/(x-4))-2 = 0
(4*x)/(x-4)-10*x^2*(x-4)^-1-2 = 0
(4*x)/(x-4)+(-10*x^2)/(x-4)-2 = 0
(4*x)/(x-4)+(-10*x^2)/(x-4)+(-2*(x-4))/(x-4) = 0
4*x-2*(x-4)-10*x^2 = 0
4*x-10*x^2-2*x+8 = 0
2*x-10*x^2+8 = 0
2*x-10*x^2+8 = 0
2*(x-5*x^2+4) = 0
x-5*x^2+4 = 0
DELTA = 1^2-(-5*4*4)
DELTA = 81
DELTA > 0
x = (81^(1/2)-1)/(-5*2) or x = (-81^(1/2)-1)/(-5*2)
x = -4/5 or x = 1
2*(x+4/5)*(x-1) = 0
(2*(x+4/5)*(x-1))/(x-4) = 0
(2*(x+4/5)*(x-1))/(x-4) = 0 // * x-4
2*(x+4/5)*(x-1) = 0
( x+4/5 )
x+4/5 = 0 // - 4/5
x = -4/5
( x-1 )
x-1 = 0 // + 1
x = 1
x in { -4/5, 1 }
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