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D( x )
x-5 = 0
x-8 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x-8 = 0
x-8 = 0
x-8 = 0 // + 8
x = 8
x in (-oo:5) U (5:8) U (8:+oo)
8/(x-5)-(8/(x-8)) = 12 // - 12
8/(x-5)-(8/(x-8))-12 = 0
8/(x-5)-8*(x-8)^-1-12 = 0
8/(x-5)-8/(x-8)-12 = 0
(8*(x-8))/((x-5)*(x-8))+(-8*(x-5))/((x-5)*(x-8))+(-12*(x-5)*(x-8))/((x-5)*(x-8)) = 0
8*(x-8)-8*(x-5)-12*(x-5)*(x-8) = 0
156*x-12*x^2-480-24 = 0
156*x-12*x^2-504 = 0
156*x-12*x^2-504 = 0
12*(13*x-x^2-42) = 0
13*x-x^2-42 = 0
DELTA = 13^2-(-42*(-1)*4)
DELTA = 1
DELTA > 0
x = (1^(1/2)-13)/(-1*2) or x = (-1^(1/2)-13)/(-1*2)
x = 6 or x = 7
12*(x-6)*(x-7) = 0
(12*(x-6)*(x-7))/((x-5)*(x-8)) = 0
(12*(x-6)*(x-7))/((x-5)*(x-8)) = 0 // * (x-5)*(x-8)
12*(x-6)*(x-7) = 0
( 12 )
12 = 0
x belongs to the empty set
( x-6 )
x-6 = 0 // + 6
x = 6
( x-7 )
x-7 = 0 // + 7
x = 7
x in { 6, 7 }
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