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D( x )
x^2-16 = 0
x+4 = 0
x-4 = 0
x^2-16 = 0
x^2-16 = 0
1*x^2 = 16 // : 1
x^2 = 16
x^2 = 16 // ^ 1/2
abs(x) = 4
x = 4 or x = -4
x+4 = 0
x+4 = 0
x+4 = 0 // - 4
x = -4
x-4 = 0
x-4 = 0
x-4 = 0 // + 4
x = 4
x in (-oo:-4) U (-4:4) U (4:+oo)
(3*x)/(x-4)+12/(x+4) = -69/(x^2-16) // + -69/(x^2-16)
(3*x)/(x-4)+12/(x+4)-(-69/(x^2-16)) = 0
(3*x)/(x-4)+12/(x+4)+69*(x^2-16)^-1 = 0
(3*x)/(x-4)+12/(x+4)+69/(x^2-16) = 0
(3*x*(x+4)*(x^2-16))/((x-4)*(x+4)*(x^2-16))+(12*(x-4)*(x^2-16))/((x-4)*(x+4)*(x^2-16))+(69*(x-4)*(x+4))/((x-4)*(x+4)*(x^2-16)) = 0
3*x*(x+4)*(x^2-16)+12*(x-4)*(x^2-16)+69*(x-4)*(x+4) = 0
3*x^4+24*x^3-96*x^2+69*x^2-384*x-1104+768 = 0
3*x^4+24*x^3-27*x^2-384*x-336 = 0
3*x^4+24*x^3-27*x^2-384*x-336 = 0
3*(x^4+8*x^3-9*x^2-128*x-112) = 0
x^4+8*x^3-9*x^2-128*x-112 = 0
{ 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 14, -14, 16, -16, 28, -28, 56, -56, 112, -112 }
1
x = 1
x^4+8*x^3-9*x^2-128*x-112 = -240
1
-1
x = -1
x^4+8*x^3-9*x^2-128*x-112 = 0
-1
x+1
x^3+7*x^2-16*x-112
x^4+8*x^3-9*x^2-128*x-112
x+1
-x^4-x^3
7*x^3-9*x^2-128*x-112
-7*x^3-7*x^2
-16*x^2-128*x-112
16*x^2+16*x
-112*x-112
112*x+112
0
x^3+7*x^2-16*x-112 = 0
{ 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 14, -14, 16, -16, 28, -28, 56, -56, 112, -112 }
1
x = 1
x^3+7*x^2-16*x-112 = -120
1
-1
x = -1
x^3+7*x^2-16*x-112 = -90
-1
2
x = 2
x^3+7*x^2-16*x-112 = -108
2
-2
x = -2
x^3+7*x^2-16*x-112 = -60
-2
4
x = 4
x^3+7*x^2-16*x-112 = 0
4
x-4
x^2+11*x+28
x^3+7*x^2-16*x-112
x-4
4*x^2-x^3
11*x^2-16*x-112
44*x-11*x^2
28*x-112
112-28*x
0
x^2+11*x+28 = 0
DELTA = 11^2-(1*4*28)
DELTA = 9
DELTA > 0
x = (9^(1/2)-11)/(1*2) or x = (-9^(1/2)-11)/(1*2)
x = -4 or x = -7
x in { -7, -4, -1, 4}
3*(x+7)*(x+4)*(x+1)*(x-4) = 0
(3*(x+7)*(x+4)*(x+1)*(x-4))/((x-4)*(x+4)*(x^2-16)) = 0
(3*(x+7)*(x+4)*(x+1)*(x-4))/((x-4)*(x+4)*(x^2-16)) = 0 // * (x-4)*(x+4)*(x^2-16)
3*(x+7)*(x+4)*(x+1)*(x-4) = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x+4 )
x+4 = 0 // - 4
x = -4
( x+7 )
x+7 = 0 // - 7
x = -7
( x-4 )
x-4 = 0 // + 4
x = 4
x in { -4}
x in { 4}
x in { -1, -7 }
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