Question

simply step by step 4+√5/4-√5 + 4-√5/4+√5​

Answer 1

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Answer 2

[tex]\mathfrak{\huge{Answer:-}} \\ \bold{\frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} }} \\ = \frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } \times \frac{4 - \sqrt{5} }{4 - \sqrt{5} } \\ = \frac{(4 + \sqrt{5})(4 + \sqrt{5})}{(4 - \sqrt{5})(4 + \sqrt{5})} + \frac{(4 - \sqrt{5})(4 - \sqrt{5})}{(4 + \sqrt{5})(4 - \sqrt{5})} \\ = \frac{ {(4 + \sqrt{5} )}^{2} }{ {(4)}^{2} - {( \sqrt{5} )}^{2} } + \frac{ {(4 - \sqrt{5} )}^{2} }{ {(4)}^{2} - {( \sqrt{5} )}^{2} } \\ = \frac{16 + 5 + 8 \sqrt{5} }{16 - 5} + \frac{16 + 5 - 8 \sqrt{5} }{16 - 5} \\ = \frac{21 + 8 \sqrt{5} }{11} + \frac{21 - 8 \sqrt{5} }{11} \\ = \frac{21 + 8 \sqrt{5} + 21 - 8 \sqrt{5} }{11} \\ = \frac{21 + 21 + 8 \sqrt{5} - 8 \sqrt{5} }{11} \\ = \frac{42}{11} \\ \boxed{\boxed{\large{\bold{ \frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } = \frac{42}{11} }}}}[/tex]