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

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


D( x )

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

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

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

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

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

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

x^3-x^2-x+1 = 0

{ 1, -1 }

1

x = 1

x^3-x^2-x+1 = 0

1

x-1

x^2-1

x^3-x^2-x+1

x-1

x^2-x^3

1-x

x-1

0

x^2-1 = 0

DELTA = 0^2-(-1*1*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)+0)/(1*2) or x = (0-4^(1/2))/(1*2)

x = 1 or x = -1

x in { -1, 1, 1} 

3 = 0

x in (-oo:-1) U (-1:1) U (1:+oo)

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

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

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

x*(5*x^2-3*x-2) = 0

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

DELTA = (-3)^2-(-2*4*5)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(2*5) or x = (3-49^(1/2))/(2*5)

x = 1 or x = -2/5

x*(x+2/5)*(x-1) = 0

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

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

x^3-x^2-x+1 = 0

{ 1, -1 }

1

x = 1

x^3-x^2-x+1 = 0

1

x-1

x^2-1

x^3-x^2-x+1

x-1

x^2-x^3

1-x

x-1

0

x^2-1 = 0

DELTA = 0^2-(-1*1*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)+0)/(1*2) or x = (0-4^(1/2))/(1*2)

x = 1 or x = -1

x in { -1, 1, 1} 

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

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

( x+2/5 )

x+2/5 = 0 // - 2/5

x = -2/5

( x-1 )

x-1 = 0 // + 1

x = 1

( x )

x = 0

x in { 1} 

x in { -2/5, 0 }

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