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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
4*x^2-(3*x) = (16*x-12)/x // - (16*x-12)/x
4*x^2-((16*x-12)/x)-(3*x) = 0
4*x^2-((16*x-12)/x)-3*x = 0
(-1*(16*x-12))/x+4*x^2-3*x = 0
(-1*(16*x-12))/x+(4*x*x^2)/x+(-3*x*x)/x = 0
4*x*x^2-1*(16*x-12)-3*x*x = 0
4*x^3-3*x^2-16*x+12 = 0
4*x^3-3*x^2-16*x+12 = 0
4*x^3-3*x^2-16*x+12 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }
1
x = 1
4*x^3-3*x^2-16*x+12 = -3
1
-1
x = -1
4*x^3-3*x^2-16*x+12 = 21
-1
2
x = 2
4*x^3-3*x^2-16*x+12 = 0
2
x-2
4*x^2+5*x-6
4*x^3-3*x^2-16*x+12
x-2
8*x^2-4*x^3
5*x^2-16*x+12
10*x-5*x^2
12-6*x
6*x-12
0
4*x^2+5*x-6 = 0
DELTA = 5^2-(-6*4*4)
DELTA = 121
DELTA > 0
x = (121^(1/2)-5)/(2*4) or x = (-121^(1/2)-5)/(2*4)
x = 3/4 or x = -2
x in { -2, 3/4, 2}
(x+2)*(x-3/4)*(x-2) = 0
((x+2)*(x-3/4)*(x-2))/x = 0
((x+2)*(x-3/4)*(x-2))/x = 0 // * x
(x+2)*(x-3/4)*(x-2) = 0
( x+2 )
x+2 = 0 // - 2
x = -2
( x-2 )
x-2 = 0 // + 2
x = 2
( x-3/4 )
x-3/4 = 0 // + 3/4
x = 3/4
x in { -2, 2, 3/4 }
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