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D( x )
x-5 = 0
x^3-125 = 0
5-x = 0
x^2+5*x+25 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x^3-125 = 0
x^3-125 = 0
1*x^3 = 125 // : 1
x^3 = 125
x^3 = 125 // ^ 1/3
x = 5
5-x = 0
5-x = 0
5-x = 0 // - 5
-x = -5 // * -1
x = 5
x^2+5*x+25 = 0
x^2+5*x+25 = 0
x^2+5*x+25 = 0
DELTA = 5^2-(1*4*25)
DELTA = -75
DELTA < 0
x in (-oo:5) U (5:+oo)
(25/(x^2+5*x+25)-(2*(x/(5-x)))-((x^3+25*x^2)/(x^3-125)))*(15*(x/(x-5))+x-5) = 0
(25/(x^2+5*x+25)-2*x*(5-x)^-1-((x^3+25*x^2)/(x^3-125)))*(15*(x/(x-5))+x-5) = 0
(25/(x^2+5*x+25)+(-2*x)/(5-x)+(-1*(x^3+25*x^2))/(x^3-125))*((15*x)/(x-5)+x-5) = 0
25/(x^2+5*x+25)+(-2*x)/(5-x)+(-1*(x^3+25*x^2))/(x^3-125) = 0
x^2+5*x+25 = 0
x^2+5*x+25 = 0
x^2+5*x+25 = 0
DELTA = 5^2-(1*4*25)
DELTA = -75
DELTA < 0
1 = 0
(-2*x)/(5-x)+(-1*(x^3+25*x^2))/(x^3-125)+25 = 0
(25*(5-x)*(x^3-125))/((5-x)*(x^3-125))+(-2*x*(x^3-125))/((5-x)*(x^3-125))+(-1*(x^3+25*x^2)*(5-x))/((5-x)*(x^3-125)) = 0
25*(5-x)*(x^3-125)-2*x*(x^3-125)-1*(x^3+25*x^2)*(5-x) = 0
x^4-27*x^4+125*x^3+20*x^3-125*x^2+3375*x-15625 = 0
145*x^3-26*x^4-125*x^2+3375*x-15625 = 0
145*x^3-26*x^4-125*x^2+3375*x-15625 = 0
145*x^3-26*x^4-125*x^2+3375*x-15625 = 0
{ 1, -1, 5, -5, 25, -25, 125, -125, 625, -625, 3125, -3125, 15625, -15625 }
1
x = 1
145*x^3-26*x^4-125*x^2+3375*x-15625 = -12256
1
-1
x = -1
145*x^3-26*x^4-125*x^2+3375*x-15625 = -19296
-1
5
x = 5
145*x^3-26*x^4-125*x^2+3375*x-15625 = 0
5
x-5
15*x^2-26*x^3-50*x+3125
145*x^3-26*x^4-125*x^2+3375*x-15625
x-5
26*x^4-130*x^3
15*x^3-125*x^2+3375*x-15625
75*x^2-15*x^3
3375*x-50*x^2-15625
50*x^2-250*x
3125*x-15625
15625-3125*x
0
15*x^2-26*x^3-50*x+3125 = 0
{ 1, -1, 5, -5, 25, -25, 125, -125, 625, -625, 3125, -3125 }
1
x = 1
15*x^2-26*x^3-50*x+3125 = 3064
1
-1
x = -1
15*x^2-26*x^3-50*x+3125 = 3216
-1
5
x = 5
15*x^2-26*x^3-50*x+3125 = 0
5
x-5
-26*x^2-115*x-625
15*x^2-26*x^3-50*x+3125
x-5
26*x^3-130*x^2
3125-115*x^2-50*x
115*x^2-575*x
3125-625*x
625*x-3125
0
-26*x^2-115*x-625 = 0
DELTA = (-115)^2-(-625*(-26)*4)
DELTA = -51775
DELTA < 0
x in { 5, 5}
(x-5)^2 = 0
((x-5)^2)/((5-x)*(x^3-125)) = 0
((x-5)^2)/((5-x)*(x^3-125)) = 0 // * (5-x)*(x^3-125)
(x-5)^2 = 0
(15*x)/(x-5)+x-5 = 0
(15*x)/(x-5)+(x*(x-5))/(x-5)+(-5*(x-5))/(x-5) = 0
x*(x-5)-5*(x-5)+15*x = 0
x^2+10*x-5*x+25 = 0
x^2+5*x+25 = 0
x^2+5*x+25 = 0
x^2+5*x+25 = 0
DELTA = 5^2-(1*4*25)
DELTA = -75
DELTA < 0
1 = 0
1/(x-5) = 0
1/(x-5) = 0 // * x-5
1 = 0
(x-5)^2 = 0
x-5 = 0 // + 5
x = 5
x in { 5}
x belongs to the empty set
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