Question
Simplify the following:$\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$
✓
Answer
$\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$
$=\frac{(4+\sqrt{5})^2+(4-\sqrt{5})^2}{(4-\sqrt{5})(4+\sqrt{5})} $
$=\frac{16+5+8 \sqrt{5}+16+5-8 \sqrt{5}}{16-5}$
$=\frac{42}{11}$
$=\frac{(4+\sqrt{5})^2+(4-\sqrt{5})^2}{(4-\sqrt{5})(4+\sqrt{5})} $
$=\frac{16+5+8 \sqrt{5}+16+5-8 \sqrt{5}}{16-5}$
$=\frac{42}{11}$
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