You can work this out with long division, by checking to see if (x2 - 1) is a factor of (2x4 + 4x3 - x2 + 4x - 3). It is. Unfortunately, the WikiAnswers system is somewhat limited in depicting things such as long division, so we won't be able to represent it here. In short though, (2x4 + 4x3 - x2 + 4x - 3) / (x2 + 1) is equal to 2x2 + 4x - 3. which means that: (x2 + 1) / (2x4 + 4x3 - x2 + 4x - 3) = (x2 + 1) / (x2 + 1)(2x2 + 4x - 3) = 1 / (2x2 + 4x - 3)
x2 + 4x = 1 x2 + 4x - 1 = 0 in the quadratic formula (b2+- Sqr(4ac))/2a, a = 1 b = 4 c = -1 so x = 8 +- i
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x2 + 4x + 3 = (x + 1)(x + 3)
4x-x2 = 2
Limx→0 [ 1 / (x - 4) + 1 / (x + 4) ] / x = Limx→0 1 / (x2 - 4x) + 1 / (x2 + 4x) = Limx→0 (x2 + 4x) / (x4 - 16x2) + (x2 - 4x) / (x4 - 16x2) = Limx→0 (x2 + 4x - 4x + x2) / (x4 - 16x2) = Limx→0 2x2 / (x4 - 16x2) = Limx→0 2 / (x2 - 16) = 2 / (0 - 16) = -1/8
2x = x2 + 4x - 3 x2 + 2x - 3 = 0 (x - 1)(x - 2) = 0
y=x2+4x+1
6
x2 + 4x + 3 = 0 (x + 1)(x + 3) = 0 x ∈ {-3, -1}
x2 + x + 6
-2