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D( x )
x-5 = 0
x+5 = 0
x^2-25 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x+5 = 0
x+5 = 0
x+5 = 0 // - 5
x = -5
x^2-25 = 0
x^2-25 = 0
1*x^2 = 25 // : 1
x^2 = 25
x^2 = 25 // ^ 1/2
abs(x) = 5
x = 5 or x = -5
x in (-oo:-5) U (-5:5) U (5:+oo)
x/(x-5)-(16/(x+5)) = 50/(x^2-25) // - 50/(x^2-25)
x/(x-5)-(16/(x+5))-(50/(x^2-25)) = 0
x/(x-5)-16*(x+5)^-1-50*(x^2-25)^-1 = 0
x/(x-5)-16/(x+5)-50/(x^2-25) = 0
(x*(x+5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-16*(x-5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-50*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0
x*(x+5)*(x^2-25)-16*(x-5)*(x^2-25)-50*(x-5)*(x+5) = 0
x^4-11*x^3+55*x^2-50*x^2+275*x-2000+1250 = 0
x^4-11*x^3+5*x^2+275*x-750 = 0
x^4-11*x^3+5*x^2+275*x-750 = 0
x^4-11*x^3+5*x^2+275*x-750 = 0
{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 25, -25, 30, -30, 50, -50, 75, -75, 125, -125, 150, -150, 250, -250, 375, -375, 750, -750 }
1
x = 1
x^4-11*x^3+5*x^2+275*x-750 = -480
1
-1
x = -1
x^4-11*x^3+5*x^2+275*x-750 = -1008
-1
2
x = 2
x^4-11*x^3+5*x^2+275*x-750 = -252
2
-2
x = -2
x^4-11*x^3+5*x^2+275*x-750 = -1176
-2
3
x = 3
x^4-11*x^3+5*x^2+275*x-750 = -96
3
-3
x = -3
x^4-11*x^3+5*x^2+275*x-750 = -1152
-3
5
x = 5
x^4-11*x^3+5*x^2+275*x-750 = 0
5
x-5
x^3-6*x^2-25*x+150
x^4-11*x^3+5*x^2+275*x-750
x-5
5*x^3-x^4
5*x^2-6*x^3+275*x-750
6*x^3-30*x^2
275*x-25*x^2-750
25*x^2-125*x
150*x-750
750-150*x
0
x^3-6*x^2-25*x+150 = 0
{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 25, -25, 30, -30, 50, -50, 75, -75, 150, -150 }
1
x = 1
x^3-6*x^2-25*x+150 = 120
1
-1
x = -1
x^3-6*x^2-25*x+150 = 168
-1
2
x = 2
x^3-6*x^2-25*x+150 = 84
2
-2
x = -2
x^3-6*x^2-25*x+150 = 168
-2
3
x = 3
x^3-6*x^2-25*x+150 = 48
3
-3
x = -3
x^3-6*x^2-25*x+150 = 144
-3
5
x = 5
x^3-6*x^2-25*x+150 = 0
5
x-5
x^2-x-30
x^3-6*x^2-25*x+150
x-5
5*x^2-x^3
150-x^2-25*x
x^2-5*x
150-30*x
30*x-150
0
x^2-x-30 = 0
DELTA = (-1)^2-(-30*1*4)
DELTA = 121
DELTA > 0
x = (121^(1/2)+1)/(1*2) or x = (1-121^(1/2))/(1*2)
x = 6 or x = -5
x in { -5, 6, 5, 5}
(x+5)*(x-6)*(x-5)^2 = 0
((x+5)*(x-6)*(x-5)^2)/((x-5)*(x+5)*(x^2-25)) = 0
((x+5)*(x-6)*(x-5)^2)/((x-5)*(x+5)*(x^2-25)) = 0 // * (x-5)*(x+5)*(x^2-25)
(x+5)*(x-6)*(x-5)^2 = 0
( x+5 )
x+5 = 0 // - 5
x = -5
( x-5 )
x-5 = 0 // + 5
x = 5
( x-6 )
x-6 = 0 // + 6
x = 6
x in { -5}
x in { 5}
x = 6
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