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D( x )
4*x+2 = 0
4*x^2-1 = 0
2*x = 0
4*x+2 = 0
4*x+2 = 0
4*x+2 = 0 // - 2
4*x = -2 // : 4
x = -2/4
x = -1/2
4*x^2-1 = 0
4*x^2-1 = 0
4*x^2 = 1 // : 4
x^2 = 1/4
x^2 = 1/4 // ^ 1/2
abs(x) = 1/2
x = 1/2 or x = -1/2
2*x = 0
2*x = 0
2*x = 0 // : 2
x = 0
x in (-oo:-1/2) U (-1/2:0) U (0:1/2) U (1/2:+oo)
3/(2*x)-(x/(4*x^2-1)) = 7/(4*x+2) // - 7/(4*x+2)
3/(2*x)-(x/(4*x^2-1))-(7/(4*x+2)) = 0
3/(2*x)-(x/(4*x^2-1))-7*(4*x+2)^-1 = 0
(-1*x)/(4*x^2-1)-7/(4*x+2)+3/(2*x) = 0
(-1*2*x*x*(4*x+2))/(2*x*(4*x^2-1)*(4*x+2))+(-7*2*x*(4*x^2-1))/(2*x*(4*x^2-1)*(4*x+2))+(3*(4*x^2-1)*(4*x+2))/(2*x*(4*x^2-1)*(4*x+2)) = 0
3*(4*x^2-1)*(4*x+2)-1*2*x*x*(4*x+2)-7*2*x*(4*x^2-1) = 0
48*x^3-64*x^3-4*x^2+24*x^2+14*x-12*x-6 = 0
20*x^2-16*x^3+2*x-6 = 0
20*x^2-16*x^3+2*x-6 = 0
2*(10*x^2-8*x^3+x-3) = 0
10*x^2-8*x^3+x-3 = 0
{ 1, -1, 3, -3 }
1
x = 1
10*x^2-8*x^3+x-3 = 0
1
x-1
2*x-8*x^2+3
10*x^2-8*x^3+x-3
x-1
8*x^3-8*x^2
2*x^2+x-3
2*x-2*x^2
3*x-3
3-3*x
0
2*x-8*x^2+3 = 0
DELTA = 2^2-(-8*3*4)
DELTA = 100
DELTA > 0
x = (100^(1/2)-2)/(-8*2) or x = (-100^(1/2)-2)/(-8*2)
x = -1/2 or x = 3/4
x in { -1/2, 3/4, 1}
2*(x+1/2)*(x-3/4)*(x-1) = 0
(2*(x+1/2)*(x-3/4)*(x-1))/(2*x*(4*x^2-1)*(4*x+2)) = 0
(2*(x+1/2)*(x-3/4)*(x-1))/(2*x*(4*x^2-1)*(4*x+2)) = 0 // * 2*x*(4*x^2-1)*(4*x+2)
2*(x+1/2)*(x-3/4)*(x-1) = 0
( x+1/2 )
x+1/2 = 0 // - 1/2
x = -1/2
( x-1 )
x-1 = 0 // + 1
x = 1
( x-3/4 )
x-3/4 = 0 // + 3/4
x = 3/4
x in { -1/2}
x in { 1, 3/4 }
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