Mostre que as funções são iguais

Mostre que as funções seguintes são iguais.

\[\begin{array}{*{20}{c}}
{\begin{array}{*{20}{c}}
{f:}&{\mathbb{R}\backslash \left\{ { – 3,3} \right\} \to \mathbb{R}} \\
{}&{x \to \frac{{x – 3}}{{{x^2} – 9}}}
\end{array}}&{}&{\text{e}}&{}&{\begin{array}{*{20}{c}}
{g:}&{\mathbb{R}\backslash \left\{ { – 3,3} \right\} \to \mathbb{R}} \\
{}&{x \to \frac{1}{{x + 3}}}
\end{array}}
\end{array}\]

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Como \[{D_f} = \mathbb{R}\backslash \left\{ { – 3,3} \right\} = {D_g}\] e \[f\left( x \right) = \frac{{x – 3}}{{{x^2} – 9}} = \frac{{x – 3}}{{\left( {x + 3} \right)\left( {x – 3} \right)}} = \frac{1}{{x + 3}} = g\left( x \right),\,\forall x \in {D_f}\] então as funções $f$ e $g$ são iguais.