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D( x )
x-5 = 0
x^2-(9*x)+20 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x^2-(9*x)+20 = 0
x^2-(9*x)+20 = 0
x^2-9*x+20 = 0
x^2-9*x+20 = 0
DELTA = (-9)^2-(1*4*20)
DELTA = 1
DELTA > 0
x = (1^(1/2)+9)/(1*2) or x = (9-1^(1/2))/(1*2)
x = 5 or x = 4
x in (-oo:4) U (4:5) U (5:+oo)
(9*x+5)/(x^2-(9*x)+20)-(9/(x-5)) = 0
(9*x+5)/(x^2-9*x+20)-9*(x-5)^-1 = 0
(9*x+5)/(x^2-9*x+20)-9/(x-5) = 0
x^2-9*x+20 = 0
x^2-9*x+20 = 0
x^2-9*x+20 = 0
DELTA = (-9)^2-(1*4*20)
DELTA = 1
DELTA > 0
x = (1^(1/2)+9)/(1*2) or x = (9-1^(1/2))/(1*2)
x = 5 or x = 4
(x-4)*(x-5) = 0
(9*x+5)/((x-4)*(x-5))-9/(x-5) = 0
(9*x+5)/((x-4)*(x-5))+(-9*(x-4))/((x-4)*(x-5)) = 0
9*x-9*(x-4)+5 = 0
41 = 0
41/((x-4)*(x-5)) = 0
41/((x-4)*(x-5)) = 0 // * (x-4)*(x-5)
41 = 0
x belongs to the empty set
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