Question

How do you evaluate `(x)/((x^2)-x)` as x approaches 0?

Answer 1

`lim_(x->0) x/(x^2-x) = -1`

Explanation:

In the given form, both the numerator and denominator are zero when `x=0`, but when `x != 0` we can divide both numerator and denominator by `x` to find:

`lim_(x->0) x/(x^2-x) = lim_(x->0)1/(x-1) = 1/(0-1) = -1`