Evaluate: \lim_{x arrow 2} ((1-\frac{2)/(x)}{x^2-4})

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Expression: $\lim_{x \rightarrow 2} \left(\frac{ 1-\frac{ 2 }{ x } }{ {x}^{2}-4 }\right)$

Since evaluating limits of the numerator and denominator would result in an indeterminate form, use the L'Hopital's rule

$\lim_{x \rightarrow 2} \left(\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 1-\frac{ 2 }{ x } \right) }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2}-4 \right) }\right)$

Find the derivative

$\lim_{x \rightarrow 2} \left(\frac{ \frac{ 2 }{ {x}^{2} } }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2}-4 \right) }\right)$

Find the derivative

$\lim_{x \rightarrow 2} \left(\frac{ \frac{ 2 }{ {x}^{2} } }{ 2x }\right)$

Simplify the complex fraction

$\lim_{x \rightarrow 2} \left(\frac{ 1 }{ {x}^{3} }\right)$

Evaluate the limit

$\frac{ 1 }{ {2}^{3} }$

Evaluate the power

$\begin{align*}&\frac{ 1 }{ 8 } \\&\begin{array} { l }0.125,& {2}^{-3}\end{array}\end{align*}$

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