(-7x+x^3+6)/(3x^2-3)

Solution for (-7x+x^3+6)/(3x^2-3) equation:

D( x )

3*x^2-3 = 0

3*x^2-3 = 0

3*x^2-3 = 0

3*x^2 = 3 // : 3

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

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

(x^3-7*x+6)/(3*x^2-3) = 0

x^3-7*x+6 = 0

x^3-7*x+6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

x^3-7*x+6 = 0

1

x-1

x^2+x-6

x^3-7*x+6

x-1

x^2-x^3

x^2-7*x+6

x-x^2

6-6*x

6*x-6

0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

x in { -3, 2, 1} 

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

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1} 

x in { -3, 2 }