4/x-2=(-4/x+2)+(24/(x-2)(x+2))

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Solution for 4/x-2=(-4/x+2)+(24/(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 = (24/(x-2))*(x+2)-4/x+2 // - (24/(x-2))*(x+2)-4/x+2

4/x-((24/(x-2))*(x+2))-(-4/x)-2-2 = 0

4/x-24*(x+2)*(x-2)^-1+4*x^-1-2-2 = 0

(-24*(x+2))/(x-2)+4/x+4/x-2-2 = 0

(-24*x*(x+2))/(x*(x-2))+(4*(x-2))/(x*(x-2))+(4*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

4*(x-2)-24*x*(x+2)+4*(x-2)-2*x*(x-2)-2*x*(x-2) = 0

4*x-24*x^2-2*x^2-2*x^2-44*x+4*x+4*x-8-8 = 0

4*x-24*x^2-2*x^2-2*x^2-40*x+4*x-16 = 0

4*x-26*x^2-2*x^2-36*x-16 = 0

-28*x^2-32*x-16 = 0

-28*x^2-32*x-16 = 0

-4*(7*x^2+8*x+4) = 0

7*x^2+8*x+4 = 0

DELTA = 8^2-(4*4*7)

DELTA = -48

DELTA < 0

-4 = 0

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

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

-4 = 0

x belongs to the empty set

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