-6/(x-8)-8/(x-3)=9

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Solution for -6/(x-8)-8/(x-3)=9 equation: 


D( x )

x-3 = 0

x-8 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:3) U (3:8) U (8:+oo)

-6/(x-8)-(8/(x-3)) = 9 // - 9

-6/(x-8)-(8/(x-3))-9 = 0

-6/(x-8)-8*(x-3)^-1-9 = 0

-6/(x-8)-8/(x-3)-9 = 0

(-6*(x-3))/((x-8)*(x-3))+(-8*(x-8))/((x-8)*(x-3))+(-9*(x-8)*(x-3))/((x-8)*(x-3)) = 0

-6*(x-3)-8*(x-8)-9*(x-8)*(x-3) = 0

99*x-9*x^2-14*x-216+82 = 0

85*x-9*x^2-134 = 0

85*x-9*x^2-134 = 0

85*x-9*x^2-134 = 0

DELTA = 85^2-(-134*(-9)*4)

DELTA = 2401

DELTA > 0

x = (2401^(1/2)-85)/(-9*2) or x = (-2401^(1/2)-85)/(-9*2)

x = 2 or x = 67/9

(x-2)*(x-67/9) = 0

((x-2)*(x-67/9))/((x-8)*(x-3)) = 0

((x-2)*(x-67/9))/((x-8)*(x-3)) = 0 // * (x-8)*(x-3)

(x-2)*(x-67/9) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-67/9 )

x-67/9 = 0 // + 67/9

x = 67/9

x in { 2, 67/9 }

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