(9x^3-15x^2+4x)/(x-3)

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Solution for (9x^3-15x^2+4x)/(x-3) equation: 


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:3) U (3:+oo)

(9*x^3-(15*x^2)+4*x)/(x-3) = 0

(9*x^3-15*x^2+4*x)/(x-3) = 0

9*x^3-15*x^2+4*x = 0

x*(9*x^2-15*x+4) = 0

9*x^2-15*x+4 = 0

DELTA = (-15)^2-(4*4*9)

DELTA = 81

DELTA > 0

x = (81^(1/2)+15)/(2*9) or x = (15-81^(1/2))/(2*9)

x = 4/3 or x = 1/3

x*(x-1/3)*(x-4/3) = 0

(x*(x-1/3)*(x-4/3))/(x-3) = 0

( x-1/3 )

x-1/3 = 0 // + 1/3

x = 1/3

( x-4/3 )

x-4/3 = 0 // + 4/3

x = 4/3

( x )

x = 0

x in { 1/3, 4/3, 0 }

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