(1/x-2)-(3/x+4)=(6/x^2+2x-8)

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Solution for (1/x-2)-(3/x+4)=(6/x^2+2x-8) 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)-4-2 = 2*x+6/(x^2)-8 // - 2*x+6/(x^2)-8

1/x-(2*x)-(3/x)-(6/(x^2))-4-2+8 = 0

1/x-2*x-3*x^-1-6*x^-2-4-2+8 = 0

2*x^0-2*x^1-2*x^-1-6*x^-2 = 0

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

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

x^2

2*x^2-2*x^3-2*x-6 = 0

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

1

x = 1

2*x^2-2*x^3-2*x-6 = -8

1

-1

x = -1

2*x^2-2*x^3-2*x-6 = 0

-1

x+1

4*x-2*x^2-6

2*x^2-2*x^3-2*x-6

x+1

2*x^3+2*x^2

4*x^2-2*x-6

-4*x^2-4*x

-6*x-6

6*x+6

0

4*x-2*x^2-6 = 0

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

DELTA = -32

DELTA < 0

x in { -1} 

x = -1

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