4/x-2=-6/x+2+6/(x-2)(x+2)

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


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

4/x-2 = (6/(x-2))*(x+2)-6/x+2 // - (6/(x-2))*(x+2)-6/x+2

4/x-((6/(x-2))*(x+2))-(-6/x)-2-2 = 0

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

(-6*(x+2))/(x-2)+4/x+6/x-2-2 = 0

(-6*x*(x+2))/(x*(x-2))+(4*(x-2))/(x*(x-2))+(6*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

4*(x-2)-6*x*(x+2)+6*(x-2)-2*x*(x-2)-2*x*(x-2) = 0

6*x-6*x^2-2*x^2-2*x^2-8*x+4*x+4*x-12-8 = 0

4*x-6*x^2-2*x^2-2*x^2-2*x+4*x-20 = 0

2*x-8*x^2-2*x^2+4*x-20 = 0

6*x-10*x^2-20 = 0

6*x-10*x^2-20 = 0

2*(3*x-5*x^2-10) = 0

3*x-5*x^2-10 = 0

DELTA = 3^2-(-10*(-5)*4)

DELTA = -191

DELTA < 0

2 = 0

2/(x*(x-2)) = 0

2/(x*(x-2)) = 0 // * x*(x-2)

2 = 0

x belongs to the empty set

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