Question 1139284
<br>
Factor numerator or denominator as appropriate in each example.<br>
1.  lim x > -1 (x^2 - 1)/ (x + 1)<br>
{{{(x^2-1)/(x+1) = ((x+1)(x-1))/(x+1)}}}<br>
The factored form shows that the rational function is equivalent to (x-1) everywhere that it is defined -- i.e., everywhere except when the denominator is zero, at x=-1.  So the limit of the rational function as x approaches -1 is (-1-1) = -2.<br>
The other two examples are very similar to that first one....<br>
2. lim x > -1 (2x^2 - x - 3)/ (x + 1)<br>
{{{2x^2-x-3 = (x+1)(2x-3)}}}...<br>
3. lim x > 3 (x - 3)/ (x^2 - 9)<br>
{{{x^2-9 = (x+3)(x-3)}}}...<br>