14/x-8-5/x-6=82/(x-6)(x-8)

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Solution for 14/x-8-5/x-6=82/(x-6)(x-8) equation: 


D( x )

x-6 = 0

x = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x = 0

x = 0

x in (-oo:0) U (0:6) U (6:+oo)

14/x-(5/x)-8-6 = (82/(x-6))*(x-8) // - (82/(x-6))*(x-8)

14/x-((82/(x-6))*(x-8))-(5/x)-8-6 = 0

14/x-82*(x-8)*(x-6)^-1-5*x^-1-8-6 = 0

(-82*(x-8))/(x-6)+14/x-5/x-8-6 = 0

(-82*x*(x-8))/(x*(x-6))+(14*(x-6))/(x*(x-6))+(-5*(x-6))/(x*(x-6))+(-8*x*(x-6))/(x*(x-6))+(-6*x*(x-6))/(x*(x-6)) = 0

14*(x-6)-82*x*(x-8)-5*(x-6)-8*x*(x-6)-6*x*(x-6) = 0

670*x-82*x^2-8*x^2-6*x^2-5*x+48*x+36*x-84+30 = 0

665*x-82*x^2-8*x^2-6*x^2+48*x+36*x-54 = 0

713*x-90*x^2-6*x^2+36*x-54 = 0

749*x-96*x^2-54 = 0

749*x-96*x^2-54 = 0

749*x-96*x^2-54 = 0

DELTA = 749^2-(-96*(-54)*4)

DELTA = 540265

DELTA > 0

x = (540265^(1/2)-749)/(-96*2) or x = (-540265^(1/2)-749)/(-96*2)

x = (11*4465^(1/2)-749)/(-192) or x = (-11*4465^(1/2)-749)/(-192)

(x-((11*4465^(1/2)-749)/(-192)))*(x-((-11*4465^(1/2)-749)/(-192))) = 0

((x-((11*4465^(1/2)-749)/(-192)))*(x-((-11*4465^(1/2)-749)/(-192))))/(x*(x-6)) = 0

((x-((11*4465^(1/2)-749)/(-192)))*(x-((-11*4465^(1/2)-749)/(-192))))/(x*(x-6)) = 0 // * x*(x-6)

(x-((11*4465^(1/2)-749)/(-192)))*(x-((-11*4465^(1/2)-749)/(-192))) = 0

( x-((-11*4465^(1/2)-749)/(-192)) )

x-((-11*4465^(1/2)-749)/(-192)) = 0 // + (-11*4465^(1/2)-749)/(-192)

x = (-11*4465^(1/2)-749)/(-192)

( x-((11*4465^(1/2)-749)/(-192)) )

x-((11*4465^(1/2)-749)/(-192)) = 0 // + (11*4465^(1/2)-749)/(-192)

x = (11*4465^(1/2)-749)/(-192)

x in { (-11*4465^(1/2)-749)/(-192), (11*4465^(1/2)-749)/(-192) }

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