5/x-2=-5/x+3+15/(x-2)(x+3)

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Solution for 5/x-2=-5/x+3+15/(x-2)(x+3) 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)

5/x-2 = (15/(x-2))*(x+3)-5/x+3 // - (15/(x-2))*(x+3)-5/x+3

5/x-((15/(x-2))*(x+3))-(-5/x)-3-2 = 0

5/x-15*(x-2)^-1*(x+3)+5*x^-1-3-2 = 0

(-15*(x+3))/(x-2)+5/x+5/x-3-2 = 0

(-15*x*(x+3))/(x*(x-2))+(5*(x-2))/(x*(x-2))+(5*(x-2))/(x*(x-2))+(-3*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

5*(x-2)-15*x*(x+3)+5*(x-2)-3*x*(x-2)-2*x*(x-2) = 0

5*x-15*x^2-3*x^2-2*x^2-40*x+6*x+4*x-10-10 = 0

6*x-15*x^2-3*x^2-2*x^2-35*x+4*x-20 = 0

4*x-18*x^2-2*x^2-29*x-20 = 0

-20*x^2-25*x-20 = 0

-20*x^2-25*x-20 = 0

-5*(4*x^2+5*x+4) = 0

4*x^2+5*x+4 = 0

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

DELTA = -39

DELTA < 0

-5 = 0

-5/(x*(x-2)) = 0

-5/(x*(x-2)) = 0 // * x*(x-2)

-5 = 0

x belongs to the empty set

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