Question

simplify the following​

Answer 1

Step-by-step explanation:

$\frac{4 + \sqrt{13} }{4 - \sqrt{13} } - \frac{4 - \sqrt{13} }{4 + \sqrt{13} } \\ = \frac{(4 + \sqrt{13} )(4 + \sqrt{13} ) - (4 - \sqrt{13} )(4 - \sqrt{13}) }{(4 - \sqrt{13} )(4 + \sqrt{13}) } \\ = \frac{(16 + 8 \sqrt{13} + 13) - (16 - 8 \sqrt{13} + 13)}{ {4}^{2} - { \sqrt{13} }^{2} } \\ = \frac{16 + 8 \sqrt{13} + 13 - 16 + 8 \sqrt{13 } - 13 }{16 - 13} \\ = \frac{16 \sqrt{13} }{3}$

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