[tex]\displaystyle\bf\\\frac{a+3b}{a^{2}-9b^{2} } =\frac{a+3b}{a^{2} -(3b)^{2} } =\frac{a+3b}{(a+3b)(a-3b)} =\frac{1}{a-3b}[/tex]
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[tex]\displaystyle\bf\\\frac{a+3b}{a^{2}-9b^{2} } =\frac{a+3b}{a^{2} -(3b)^{2} } =\frac{a+3b}{(a+3b)(a-3b)} =\frac{1}{a-3b}[/tex]