(1/x-2)+(3/x+3)=(4/x^2+x-6)

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Solution for (1/x-2)+(3/x+3)=(4/x^2+x-6) equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/x+3/x-2+3 = x+4/(x^2)-6 // - x+4/(x^2)-6

1/x-x+3/x-(4/(x^2))-2+3+6 = 0

1/x-x+3/x-4*x^-2-2+3+6 = 0

4*x^-1-1*x^1-4*x^-2+7*x^0 = 0

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

x^2*(7*x^2-1*x^3+4*x^1-4*x^0) = 0

x^2

7*x^2-x^3+4*x-4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

7*x^2-x^3+4*x-4 = 6

1

-1

x = -1

7*x^2-x^3+4*x-4 = 0

-1

x+1

8*x-x^2-4

7*x^2-x^3+4*x-4

x+1

x^3+x^2

8*x^2+4*x-4

-8*x^2-8*x

-4*x-4

4*x+4

0

8*x-x^2-4 = 0

DELTA = 8^2-(-4*(-1)*4)

DELTA = 48

DELTA > 0

x = (48^(1/2)-8)/(-1*2) or x = (-48^(1/2)-8)/(-1*2)

x = (4*3^(1/2)-8)/(-2) or x = (-4*3^(1/2)-8)/(-2)

x in { (4*3^(1/2)-8)/(-2), (-4*3^(1/2)-8)/(-2), -1} 

x in { (4*3^(1/2)-8)/(-2), (-4*3^(1/2)-8)/(-2), -1 }

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