Question

What is the result of this:
lim(x->1) (1 - x^2 / x^4 - x)

Answer 1

factor x in the denominator and write x^3-1 as x^3-1^3

Answer 2

use a^3-b^3 identity to factor (x-1) again

Answer 3

Denominator :
x^4 - x = x(x^3-1^3) = x(x-1)(x^2+x+1)

Answer 4

Numerator :
1-x^2 = 1^2 - x^2 = -(x+1)(x-1)

Answer 5

plug them, cancel the common factors and take the limit