4/x-3=-6/x+5+12/(x-3)(x+5)

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Solution for 4/x-3=-6/x+5+12/(x-3)(x+5) equation: 


D( x )

x = 0

x-3 = 0

x = 0

x = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:0) U (0:3) U (3:+oo)

4/x-3 = (12/(x-3))*(x+5)-6/x+5 // - (12/(x-3))*(x+5)-6/x+5

4/x-((12/(x-3))*(x+5))-(-6/x)-5-3 = 0

4/x-12*(x-3)^-1*(x+5)+6*x^-1-5-3 = 0

(-12*(x+5))/(x-3)+4/x+6/x-5-3 = 0

(-12*x*(x+5))/(x*(x-3))+(4*(x-3))/(x*(x-3))+(6*(x-3))/(x*(x-3))+(-5*x*(x-3))/(x*(x-3))+(-3*x*(x-3))/(x*(x-3)) = 0

4*(x-3)-12*x*(x+5)+6*(x-3)-5*x*(x-3)-3*x*(x-3) = 0

6*x-12*x^2-5*x^2-3*x^2-56*x+15*x+9*x-18-12 = 0

15*x-12*x^2-5*x^2-3*x^2-50*x+9*x-30 = 0

9*x-17*x^2-3*x^2-35*x-30 = 0

-20*x^2-26*x-30 = 0

-20*x^2-26*x-30 = 0

-2*(10*x^2+13*x+15) = 0

10*x^2+13*x+15 = 0

DELTA = 13^2-(4*10*15)

DELTA = -431

DELTA < 0

-2 = 0

-2/(x*(x-3)) = 0

-2/(x*(x-3)) = 0 // * x*(x-3)

-2 = 0

x belongs to the empty set

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