(6x-18)/(x^2-x-6)=x

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Solution for (6x-18)/(x^2-x-6)=x equation: 


D( x )

x^2-x-6 = 0

x^2-x-6 = 0

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

x = 3 or x = -2

x in (-oo:-2) U (-2:3) U (3:+oo)

(6*x-18)/(x^2-x-6) = x // - x

(6*x-18)/(x^2-x-6)-x = 0

x^2-x-6 = 0

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

x = 3 or x = -2

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

(6*x-18)/((x+2)*(x-3))-x = 0

(6*x-18)/((x+2)*(x-3))+(-x*(x+2)*(x-3))/((x+2)*(x-3)) = 0

6*x-x*(x+2)*(x-3)-18 = 0

x^2-x^3+12*x-18 = 0

x^2-x^3+12*x-18 = 0

x^2-x^3+12*x-18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

x = 1

x^2-x^3+12*x-18 = -6

1

-1

x = -1

x^2-x^3+12*x-18 = -28

-1

2

x = 2

x^2-x^3+12*x-18 = 2

2

-2

x = -2

x^2-x^3+12*x-18 = -30

-2

3

x = 3

x^2-x^3+12*x-18 = 0

3

x-3

6-x^2-2*x

x^2-x^3+12*x-18

x-3

x^3-3*x^2

12*x-2*x^2-18

2*x^2-6*x

6*x-18

18-6*x

0

6-x^2-2*x = 0

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

DELTA = 28

DELTA > 0

x = (28^(1/2)+2)/(-1*2) or x = (2-28^(1/2))/(-1*2)

x = (2*7^(1/2)+2)/(-2) or x = (2-2*7^(1/2))/(-2)

x in { (2*7^(1/2)+2)/(-2), (2-2*7^(1/2))/(-2), 3} 

(x-((2*7^(1/2)+2)/(-2)))*(x-((2-2*7^(1/2))/(-2)))*(x-3) = 0

((x-((2*7^(1/2)+2)/(-2)))*(x-((2-2*7^(1/2))/(-2)))*(x-3))/((x+2)*(x-3)) = 0

((x-((2*7^(1/2)+2)/(-2)))*(x-((2-2*7^(1/2))/(-2)))*(x-3))/((x+2)*(x-3)) = 0 // * (x+2)*(x-3)

(x-((2*7^(1/2)+2)/(-2)))*(x-((2-2*7^(1/2))/(-2)))*(x-3) = 0

( x-((2*7^(1/2)+2)/(-2)) )

x-((2*7^(1/2)+2)/(-2)) = 0 // + (2*7^(1/2)+2)/(-2)

x = (2*7^(1/2)+2)/(-2)

( x-((2-2*7^(1/2))/(-2)) )

x-((2-2*7^(1/2))/(-2)) = 0 // + (2-2*7^(1/2))/(-2)

x = (2-2*7^(1/2))/(-2)

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x in { (2*7^(1/2)+2)/(-2), (2-2*7^(1/2))/(-2) }

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