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D( x )
x^2-(3*x)-10 = 0
3*x-15 = 0
4*x+8 = 0
x^2-(3*x)-10 = 0
x^2-(3*x)-10 = 0
x^2-3*x-10 = 0
x^2-3*x-10 = 0
DELTA = (-3)^2-(-10*1*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)
x = 5 or x = -2
3*x-15 = 0
3*x-15 = 0
3*x-15 = 0 // + 15
3*x = 15 // : 3
x = 15/3
x = 5
4*x+8 = 0
4*x+8 = 0
4*x+8 = 0 // - 8
4*x = -8 // : 4
x = -8/4
x = -2
x in (-oo:-2) U (-2:5) U (5:+oo)
5/(x^2-(3*x)-10)-(2/(3*x-15)) = 3/(4*x+8) // - 3/(4*x+8)
5/(x^2-(3*x)-10)-(2/(3*x-15))-(3/(4*x+8)) = 0
5/(x^2-3*x-10)-2*(3*x-15)^-1-3*(4*x+8)^-1 = 0
5/(x^2-3*x-10)-2/(3*x-15)-3/(4*x+8) = 0
x^2-3*x-10 = 0
x^2-3*x-10 = 0
x^2-3*x-10 = 0
DELTA = (-3)^2-(-10*1*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)
x = 5 or x = -2
(x+2)*(x-5) = 0
5/((x+2)*(x-5))-2/(3*x-15)-3/(4*x+8) = 0
(5*(3*x-15)*(4*x+8))/((x+2)*(x-5)*(3*x-15)*(4*x+8))+(-2*(x+2)*(x-5)*(4*x+8))/((x+2)*(x-5)*(3*x-15)*(4*x+8))+(-3*(x+2)*(x-5)*(3*x-15))/((x+2)*(x-5)*(3*x-15)*(4*x+8)) = 0
5*(3*x-15)*(4*x+8)-2*(x+2)*(x-5)*(4*x+8)-3*(x+2)*(x-5)*(3*x-15) = 0
68*x^2-8*x^3-9*x^3+72*x^2-52*x-45*x-450-440 = 0
140*x^2-17*x^3-97*x-890 = 0
140*x^2-17*x^3-97*x-890 = 0
140*x^2-17*x^3-97*x-890 = 0
{ 1, -1, 2, -2, 5, -5, 10, -10, 89, -89, 178, -178, 445, -445, 890, -890 }
1
x = 1
140*x^2-17*x^3-97*x-890 = -864
1
-1
x = -1
140*x^2-17*x^3-97*x-890 = -636
-1
2
x = 2
140*x^2-17*x^3-97*x-890 = -660
2
-2
x = -2
140*x^2-17*x^3-97*x-890 = 0
-2
x+2
174*x-17*x^2-445
140*x^2-17*x^3-97*x-890
x+2
17*x^3+34*x^2
174*x^2-97*x-890
-174*x^2-348*x
-445*x-890
445*x+890
0
174*x-17*x^2-445 = 0
DELTA = 174^2-(-445*(-17)*4)
DELTA = 16
DELTA > 0
x = (16^(1/2)-174)/(-17*2) or x = (-16^(1/2)-174)/(-17*2)
x = 5 or x = 89/17
x in { 5, 89/17, -2}
(x-5)*(x-89/17)*(x+2) = 0
((x-5)*(x-89/17)*(x+2))/((x+2)*(x-5)*(3*x-15)*(4*x+8)) = 0
((x-5)*(x-89/17)*(x+2))/((x+2)*(x-5)*(3*x-15)*(4*x+8)) = 0 // * (x+2)*(x-5)*(3*x-15)*(4*x+8)
(x-5)*(x-89/17)*(x+2) = 0
( x+2 )
x+2 = 0 // - 2
x = -2
( x-5 )
x-5 = 0 // + 5
x = 5
( x-89/17 )
x-89/17 = 0 // + 89/17
x = 89/17
x in { -2}
x in { 5}
x = 89/17
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