9/x^2-6x+9=3x/x^2-3x

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Solution for 9/x^2-6x+9=3x/x^2-3x equation:


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

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

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

3*x-6*x-3*x^-1+9/(x^2)+9 = 0

9*x^-2-3*x^1-3*x^-1+9*x^0 = 0

(9*x^2-3*x^3-3*x^1+9*x^0)/(x^2) = 0 // * x^4

x^2*(9*x^2-3*x^3-3*x^1+9*x^0) = 0

x^2

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

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

1

x = 1

9*x^2-3*x^3-3*x+9 = 12

1

-1

x = -1

9*x^2-3*x^3-3*x+9 = 24

-1

3

x = 3

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

3

x-3

-3*x^2-3

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

x-3

3*x^3-9*x^2

9-3*x

3*x-9

0

-3*x^2-3 = 0

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

DELTA = -36

DELTA < 0

x in { 3}

x = 3

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