Help finding the limit

How would you find the limit as x approaches -1 for the equation (x^2-1)/(|x|-1). I'm just not sure how to get rid of the absolute value at in the denominator.

Note that x^2 = |x|^2.

So, lim(x→ -1) (x^2 - 1) / (|x| - 1)
= lim(x→ -1) (|x|^2 - 1) / (|x| - 1)
= lim(x→ -1) (|x| + 1)(|x| - 1) / (|x| - 1)
= lim(x→ -1) (|x| + 1)
= |-1| + 1
= 2.
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Alternately, since x < 0, we have |x| = -x.

So, lim(x→ -1) (x^2 - 1) / (|x| - 1)
= lim(x→ -1) (x^2 - 1) / (-x - 1)
= lim(x→ -1) (x - 1)(x + 1) / [-(x + 1)]
= lim(x→ -1) -(x - 1)
= -(-1 - 1)
= 2.

I hope this helps!