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Rationalization Method to Remove Indeterminate Form

Show that l...

Question

Show that ${lim}_{x \to 2} \frac{x^{2} - 5 x + 6}{x^{2} - x - 2} = \frac{- 1}{3}$

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Solution

Let $L = {lim}_{x \to 2} \frac{x^{2} - 5 x + 6}{x^{2} - x - 2}$
This is $\frac{0}{0}$ form.
Therefore by using L'Hospital rule
$L = {lim}_{x \to 2} \frac{2 x - 5}{2 x - 1} \Rightarrow L = \frac{2 (2) - 5}{2 (2) - 1} \Rightarrow L = - \frac{1}{3}$

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