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D( x )
x-7 = 0
x-9 = 0
x-7 = 0
x-7 = 0
x-7 = 0 // + 7
x = 7
x-9 = 0
x-9 = 0
x-9 = 0 // + 9
x = 9
x in (-oo:7) U (7:9) U (9:+oo)
6/(x-9)-(9/(x-7)) = -15 // + 15
6/(x-9)-(9/(x-7))+15 = 0
6/(x-9)-9*(x-7)^-1+15 = 0
6/(x-9)-9/(x-7)+15 = 0
(6*(x-7))/((x-9)*(x-7))+(-9*(x-9))/((x-9)*(x-7))+(15*(x-9)*(x-7))/((x-9)*(x-7)) = 0
6*(x-7)-9*(x-9)+15*(x-9)*(x-7) = 0
15*x^2-3*x-240*x+39+945 = 0
15*x^2-243*x+984 = 0
15*x^2-243*x+984 = 0
3*(5*x^2-81*x+328) = 0
5*x^2-81*x+328 = 0
DELTA = (-81)^2-(4*5*328)
DELTA = 1
DELTA > 0
x = (1^(1/2)+81)/(2*5) or x = (81-1^(1/2))/(2*5)
x = 41/5 or x = 8
3*(x-8)*(x-41/5) = 0
(3*(x-8)*(x-41/5))/((x-9)*(x-7)) = 0
(3*(x-8)*(x-41/5))/((x-9)*(x-7)) = 0 // * (x-9)*(x-7)
3*(x-8)*(x-41/5) = 0
( 3 )
3 = 0
x belongs to the empty set
( x-41/5 )
x-41/5 = 0 // + 41/5
x = 41/5
( x-8 )
x-8 = 0 // + 8
x = 8
x in { 41/5, 8 }
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