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[tex] \frac{4}{ \sqrt{13} - 3} = \frac{4}{ \sqrt{13} - 3} \times \frac{ \sqrt{13} + 3 }{ \sqrt{13} + 3} = \frac{4( \sqrt{13} + 3)}{( \sqrt{13} - 3)( \sqrt{13} + 3) } = \frac{4( \sqrt{13} + 3) }{ { \sqrt{13} }^{2} - {3}^{2} } = \frac{4( \sqrt{13} + 3)}{13 - 9} = \frac{4( \sqrt{13} + 3) }{4} = \sqrt{13} + 3 \\ [/tex]