Original
Note that
{{MATH_108}}
Our limit is, again, of the form {{CMD_109}}{{CMD_110}}and we
can probably factor a term going to {{MATH_111}} out of both the numerator
and denominator. We suspect from looking at the denominator that
this term is {{MATH_112}}. Unfortunately, it is not immediately obvious
how to factor an {{MATH_113}} out of the numerator.
We will use an algebraic technique called {{CMD_114}}. This technique is useful when you are trying to
simplify an expression that looks like
{{MATH_115}}
It takes advantage of the difference of squares rule
{{MATH_116}}
In our case, we will use {{MATH_117}} and {{MATH_118}}. Write
{{MATH_119}}
{{ENV_120}}
{{CMD_121}}
{{CMD_122}}