V3 4+55 4-15 Simplify 4-55 4+55 1
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V3 4+55 4-15 Simplify 4-55 4+55 1

JEE/Engineering Exams
Maths
Solution
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( begin{aligned} frac{4+sqrt{5}}{4-sqrt{5}}+frac{4-sqrt{5}}{4+sqrt{5}} &=frac{(4+sqrt{5})^{2}+(4-sqrt{5})^{2}}{(4-sqrt{5})(4+sqrt{5})} &=16+5+frac{8 sqrt{5}+16+5-8 sqrt{5}}{16-5} &=frac{42}{11} end{aligned} )
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