# Calculate: \lim_{x arrow 2} ((x-2)/(x^2-4))

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

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

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

Find the derivative

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

Find the derivative

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

Evaluate the limit

$\frac{ 1 }{ 2 \times 2 }$

Multiply the numbers

\begin{align*}&\frac{ 1 }{ 4 } \\&\begin{array} { l }0.25,& {2}^{-2}\end{array}\end{align*}

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