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D( x )
10*x^2-(13*x)-3 = 0
5*x+1 = 0
2*x-3 = 0
10*x^2-(13*x)-3 = 0
10*x^2-(13*x)-3 = 0
10*x^2-13*x-3 = 0
10*x^2-13*x-3 = 0
DELTA = (-13)^2-(-3*4*10)
DELTA = 289
DELTA > 0
x = (289^(1/2)+13)/(2*10) or x = (13-289^(1/2))/(2*10)
x = 3/2 or x = -1/5
5*x+1 = 0
5*x+1 = 0
5*x+1 = 0 // - 1
5*x = -1 // : 5
x = -1/5
2*x-3 = 0
2*x-3 = 0
2*x-3 = 0 // + 3
2*x = 3 // : 2
x = 3/2
x in (-oo:-1/5) U (-1/5:3/2) U (3/2:+oo)
2/(2*x-3)-(2/(10*x^2-(13*x)-3)) = x/(5*x+1) // - x/(5*x+1)
2/(2*x-3)-(2/(10*x^2-(13*x)-3))-(x/(5*x+1)) = 0
2/(2*x-3)-2*(10*x^2-13*x-3)^-1-(x/(5*x+1)) = 0
2/(2*x-3)-2/(10*x^2-13*x-3)+(-1*x)/(5*x+1) = 0
10*x^2-13*x-3 = 0
10*x^2-13*x-3 = 0
10*x^2-13*x-3 = 0
DELTA = (-13)^2-(-3*4*10)
DELTA = 289
DELTA > 0
x = (289^(1/2)+13)/(2*10) or x = (13-289^(1/2))/(2*10)
x = 3/2 or x = -1/5
(x+1/5)*(x-3/2) = 0
2/(2*x-3)-2/((x+1/5)*(x-3/2))+(-1*x)/(5*x+1) = 0
(2*(x+1/5)*(x-3/2)*(5*x+1))/((2*x-3)*(x+1/5)*(x-3/2)*(5*x+1))+(-2*(2*x-3)*(5*x+1))/((2*x-3)*(x+1/5)*(x-3/2)*(5*x+1))+(-1*x*(2*x-3)*(x+1/5)*(x-3/2))/((2*x-3)*(x+1/5)*(x-3/2)*(5*x+1)) = 0
2*(x+1/5)*(x-3/2)*(5*x+1)-2*(2*x-3)*(5*x+1)-1*x*(2*x-3)*(x+1/5)*(x-3/2) = 0
10*x^3-2*x^4+28/5*x^3-31*x^2-33/10*x^2+102/5*x-9/10*x+27/5 = 0
78/5*x^3-2*x^4-343/10*x^2+39/2*x+27/5 = 0
78/5*x^3-2*x^4-343/10*x^2+39/2*x+27/5 = 0
(78/5)*x^3-2*x^4+(-343/10)*x^2+(39/2)*x+27/5 = 0
(78/5)*x^3-2*x^4+(-343/10)*x^2+(39/2)*x+27/5 = 0 // * 0
{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18, 27, -27, 54, -54 }
1
x = 1
156*x^3-20*x^4-343*x^2+195*x+54 = 42
1
-1
x = -1
156*x^3-20*x^4-343*x^2+195*x+54 = -660
-1
2
x = 2
156*x^3-20*x^4-343*x^2+195*x+54 = 0
2
x-2
116*x^2-20*x^3-111*x-27
156*x^3-20*x^4-343*x^2+195*x+54
x-2
20*x^4-40*x^3
116*x^3-343*x^2+195*x+54
232*x^2-116*x^3
195*x-111*x^2+54
111*x^2-222*x
54-27*x
27*x-54
0
116*x^2-20*x^3-111*x-27 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27 }
1
x = 1
116*x^2-20*x^3-111*x-27 = -42
1
-1
x = -1
116*x^2-20*x^3-111*x-27 = 220
-1
3
x = 3
116*x^2-20*x^3-111*x-27 = 144
3
-3
x = -3
116*x^2-20*x^3-111*x-27 = 1890
-3
9
x = 9
116*x^2-20*x^3-111*x-27 = -6210
9
-9
x = -9
116*x^2-20*x^3-111*x-27 = 24948
-9
27
x = 27
116*x^2-20*x^3-111*x-27 = -312120
27
-27
x = -27
116*x^2-20*x^3-111*x-27 = 481194
-27
{ 1/2, -1/2, 1/4, -1/4, 1/5, -1/5, 1/10, -1/10, 1/20, -1/20, -1/2, 1/2, -1/4, 1/4, -1/5, 1/5, -1/10, 1/10, -1/20, 1/20, 3/2, -3/2, 3/4, -3/4, 3/5, -3/5, 3/10, -3/10, 3/20, -3/20, -3/2, 3/2, -3/4, 3/4, -3/5, 3/5, -3/10, 3/10, -3/20, 3/20, 9/2, -9/2, 9/4, -9/4, 9/5, -9/5, 9/10, -9/10, 9/20, -9/20, -9/2, 9/2, -9/4, 9/4, -9/5, 9/5, -9/10, 9/10, -9/20, 9/20, 27/2, -27/2, 27/4, -27/4, 27/5, -27/5, 27/10, -27/10, 27/20, -27/20, -27/2, 27/2, -27/4, 27/4, -27/5, 27/5, -27/10, 27/10, -27/20, 27/20 }
1/2
x
1/2
116*x^2-20*x^3-111*x-27 = -56
1/2
-1/2
x
-1/2
116*x^2-20*x^3-111*x-27 = 60
-1/2
1/4
x
1/4
116*x^2-20*x^3-111*x-27 = -47.8125
1/4
-1/4
x
-1/4
116*x^2-20*x^3-111*x-27 = 8.3125
-1/4
1/5
x
1/5
116*x^2-20*x^3-111*x-27 = -44.72
1/5
-1/5
x
-1/5
116*x^2-20*x^3-111*x-27 = 0
-1/5
x+1/5
120*x-20*x^2-135
116*x^2-20*x^3-111*x-27
x+1/5
20*x^3+4*x^2
120*x^2-111*x-27
-120*x^2-24*x
-135*x-27
135*x+27
0
120*x-20*x^2-135 = 0
DELTA = 120^2-(-135*(-20)*4)
DELTA = 3600
DELTA > 0
x = (3600^(1/2)-120)/(-20*2) or x = (-3600^(1/2)-120)/(-20*2)
x = 3/2 or x = 9/2
x in { 3/2, 9/2, 2, -1/5}
(x-3/2)*(x-9/2)*(x-2)*(x+1/5) = 0
((x-3/2)*(x-9/2)*(x-2)*(x+1/5))/((2*x-3)*(x+1/5)*(x-3/2)*(5*x+1)) = 0
((x-3/2)*(x-9/2)*(x-2)*(x+1/5))/((2*x-3)*(x+1/5)*(x-3/2)*(5*x+1)) = 0 // * (2*x-3)*(x+1/5)*(x-3/2)*(5*x+1)
(x-3/2)*(x-9/2)*(x-2)*(x+1/5) = 0
( x+1/5 )
x+1/5 = 0 // - 1/5
x = -1/5
( x-2 )
x-2 = 0 // + 2
x = 2
( x-3/2 )
x-3/2 = 0 // + 3/2
x = 3/2
( x-9/2 )
x-9/2 = 0 // + 9/2
x = 9/2
x in { -1/5}
x in { 3/2}
x in { 2, 9/2 }
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