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\[\frac{ \sqrt{x+5}-4 }{ x-11 }\] this is as x approaches 11
gimmick is to rationalize the numerator
rationalize the numerator

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leave the denominator in factored form, i.e don't multiply out
Multiply by \(\frac{\sqrt{x+5}+4}{\sqrt{x+5}+4}\)
\[ \frac{ x+5 + 16}{ x-11 (\sqrt{x+5})}\]
\[\frac{ x+21 }{ x-11\sqrt{x+5} }\]
Then I would plug in the the value and solve, correct?
Check your multiplication. You need to expand the numerator, but no need to expand the denominator.
\[\frac{ \sqrt{x+5}-4 }{ x-11 } \times \frac{\sqrt{x+5}+4}{\sqrt{x+5}+4}\]

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