x^2/(2x-6)-9/(6x-18)

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Solution for x^2/(2x-6)-9/(6x-18) equation:


D( x )

6*x-18 = 0

2*x-6 = 0

6*x-18 = 0

6*x-18 = 0

6*x-18 = 0 // + 18

6*x = 18 // : 6

x = 18/6

x = 3

2*x-6 = 0

2*x-6 = 0

2*x-6 = 0 // + 6

2*x = 6 // : 2

x = 6/2

x = 3

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

(x^2)/(2*x-6)-(9/(6*x-18)) = 0

(x^2)/(2*x-6)-9*(6*x-18)^-1 = 0

(x^2)/(2*x-6)-9/(6*x-18) = 0

(x^2*(6*x-18))/((2*x-6)*(6*x-18))+(-9*(2*x-6))/((2*x-6)*(6*x-18)) = 0

x^2*(6*x-18)-9*(2*x-6) = 0

6*x^3-18*x^2-18*x+54 = 0

6*x^3-18*x^2-18*x+54 = 0

6*(x^3-3*x^2-3*x+9) = 0

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

{ 1, -1, 3, -3, 9, -9 }

1

x = 1

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

1

-1

x = -1

x^3-3*x^2-3*x+9 = 8

-1

3

x = 3

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

3

x-3

x^2-3

x^3-3*x^2-3*x+9

x-3

3*x^2-x^3

9-3*x

3*x-9

0

x^2-3 = 0

DELTA = 0^2-(-3*1*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)+0)/(1*2) or x = (0-12^(1/2))/(1*2)

x = 3^(1/2) or x = -3^(1/2)

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

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

(6*(x+3^(1/2))*(x-3^(1/2))*(x-3))/((2*x-6)*(6*x-18)) = 0

(6*(x+3^(1/2))*(x-3^(1/2))*(x-3))/((2*x-6)*(6*x-18)) = 0 // * (2*x-6)*(6*x-18)

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

( 6 )

6 = 0

x belongs to the empty set

( x+3^(1/2) )

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

x = -3^(1/2)

( x-3 )

x-3 = 0 // + 3

x = 3

( x-3^(1/2) )

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

x = 3^(1/2)

x in { 3}

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

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