Another Limit Problem

[Jason76]

\(\displaystyle \lim \dfrac{1 - x^{2} }{x^{4} - x }\)

as x approaches 1.

The book says the answer is \(\displaystyle -\dfrac{2}{3}\)

If you plug in 1 into everything then it comes out as 0/0 or indeterminate. So the way out must be some kind of factoring.

 

[Deleted member 4993]

\(\displaystyle \lim \dfrac{1 - x^{2} }{x^{4} - x }\)

as x approaches 1.

The book says the answer is \(\displaystyle -\dfrac{2}{3}\)

If you plug in 1 into everything then it comes out as 0/0 or indeterminate. So the way out must be some kind of factoring.

x⁴ - x = x(x³ - 1) = x (x-1)(x² + x + 1)

1 - x² = (1 - x)(1 + x)