(x^3-6x^2+3x-1)/(x-5)

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Solution for (x^3-6x^2+3x-1)/(x-5) equation: 


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x in (-oo:5) U (5:+oo)

t_2 = 0

(x^3-6*x^2+3*x-1)/(x-5)+t_2 = 0

(x^3-6*x^2+3*x-1)/(x-5)+(t_2*(x-5))/(x-5) = 0

t_2*(x-5)+x^3-6*x^2+3*x-1 = 0

t_2*x-5*t_2+x^3-6*x^2+3*x-1 = 0

t_2*x-5*t_2+x^3-6*x^2+3*x-1 = 0

t_2*x-5*t_2+x^3-6*x^2+3*x-1

x*(x^2+3)+t_2*x-5*t_2-6*x^2-1

x*(t_2-6*x)+x*(x^2+3)-5*t_2-1

x*(t_2-6*x)-1*(5*t_2+1)+x*(x^2+3)

x*(t_2+x^2-6*x+3)-1*(5*t_2+1)

0*(t_2+x^2-6*x+3)

(0*(t_2+x^2-6*x+3))/(x-5) = 0

(0*(t_2+x^2-6*x+3))/(x-5) = 0 // * x-5

0*(t_2+x^2-6*x+3) = 0

t_2+x^2-6*x+3 = 0

DELTA = (-6)^2-(1*4*(t_2+3))

DELTA = 36-4*(t_2+3)

36-4*(t_2+3) = 0

36-4*(t_2+3) = 0

24-4*t_2 = 0

24-4*t_2 = 0

24-4*t_2 = 0 // - 24

-4*t_2 = -24 // : -4

t_2 = -24/(-4)

t_2 = 6

DELTA = 0  <=>  t_4 = 6

x = 6/(1*2) i t_2 = 6

x = 3 i t_2 = 6

( x = ((36-4*(t_2+3))^(1/2)+6)/(1*2) or x = (6-(36-4*(t_2+3))^(1/2))/(1*2) ) i t_2 > 6

( x = ((36-4*(t_2+3))^(1/2)+6)/2 or x = (6-(36-4*(t_2+3))^(1/2))/2 ) i t_2 > 6

t_2-6 > 0

t_2-6 > 0 // + 6

t_2 > 6

x in { 3, ((36-4*(0+3))^(1/2)+6)/2, (6-(36-4*(0+3))^(1/2))/2 }

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