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D( x )
x+100 = 0
x+100 = 0
x+100 = 0
x+100 = 0 // - 100
x = -100
x in (-oo:-100) U (-100:+oo)
(x^2)/(x+100) = 50 // - 50
(x^2)/(x+100)-50 = 0
(x^2)/(x+100)+(-50*(x+100))/(x+100) = 0
x^2-50*(x+100) = 0
x^2-50*x-5000 = 0
x^2-50*x-5000 = 0
x^2-50*x-5000 = 0
DELTA = (-50)^2-(-5000*1*4)
DELTA = 22500
DELTA > 0
x = (22500^(1/2)+50)/(1*2) or x = (50-22500^(1/2))/(1*2)
x = 100 or x = -50
(x+50)*(x-100) = 0
((x+50)*(x-100))/(x+100) = 0
((x+50)*(x-100))/(x+100) = 0 // * x+100
(x+50)*(x-100) = 0
( x+50 )
x+50 = 0 // - 50
x = -50
( x-100 )
x-100 = 0 // + 100
x = 100
x in { -50, 100 }
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