Question

How to prove: lim (x->0) (x^2 - x) / (x) = -1?

Answer 1

Separate it into two fractions. For every term in the numerator, you can make it into its own fraction over the denominator:

\[\frac{ x^{2}-x }{ x }= \frac{ x^{2} }{ x }-\frac{ x }{ x } \]

Or you can simply factor an x out of the numerator and not need to break it up at all:

\[\frac{ x^{2}-x }{ x }=\frac{ x(x-1) }{ x }\]

Answer 2

Perfect! Thank You!