6/x-2=-5/x+6+37/(x-2)(x+6)

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Solution for 6/x-2=-5/x+6+37/(x-2)(x+6) 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)

6/x-2 = (37/(x-2))*(x+6)-5/x+6 // - (37/(x-2))*(x+6)-5/x+6

6/x-((37/(x-2))*(x+6))-(-5/x)-6-2 = 0

6/x-37*(x-2)^-1*(x+6)+5*x^-1-6-2 = 0

(-37*(x+6))/(x-2)+6/x+5/x-6-2 = 0

(-37*x*(x+6))/(x*(x-2))+(6*(x-2))/(x*(x-2))+(5*(x-2))/(x*(x-2))+(-6*x*(x-2))/(x*(x-2))+(-2*x*(x-2))/(x*(x-2)) = 0

6*(x-2)-37*x*(x+6)+5*(x-2)-6*x*(x-2)-2*x*(x-2) = 0

5*x-37*x^2-6*x^2-2*x^2-216*x+12*x+4*x-12-10 = 0

12*x-37*x^2-6*x^2-2*x^2-211*x+4*x-22 = 0

4*x-43*x^2-2*x^2-199*x-22 = 0

-45*x^2-195*x-22 = 0

-45*x^2-195*x-22 = 0

-1*(45*x^2+195*x+22) = 0

45*x^2+195*x+22 = 0

DELTA = 195^2-(4*22*45)

DELTA = 34065

DELTA > 0

x = (34065^(1/2)-195)/(2*45) or x = (-34065^(1/2)-195)/(2*45)

x = (3*3785^(1/2)-195)/90 or x = (-3*3785^(1/2)-195)/90

-1*(x-((-3*3785^(1/2)-195)/90))*(x-((3*3785^(1/2)-195)/90)) = 0

(-1*(x-((-3*3785^(1/2)-195)/90))*(x-((3*3785^(1/2)-195)/90)))/(x*(x-2)) = 0

(-1*(x-((-3*3785^(1/2)-195)/90))*(x-((3*3785^(1/2)-195)/90)))/(x*(x-2)) = 0 // * x*(x-2)

-1*(x-((-3*3785^(1/2)-195)/90))*(x-((3*3785^(1/2)-195)/90)) = 0

( x-((-3*3785^(1/2)-195)/90) )

x-((-3*3785^(1/2)-195)/90) = 0 // + (-3*3785^(1/2)-195)/90

x = (-3*3785^(1/2)-195)/90

( x-((3*3785^(1/2)-195)/90) )

x-((3*3785^(1/2)-195)/90) = 0 // + (3*3785^(1/2)-195)/90

x = (3*3785^(1/2)-195)/90

x in { (-3*3785^(1/2)-195)/90, (3*3785^(1/2)-195)/90 }

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