Question

simplify:7+.3root5/3+root5 - 7-3root5/3-root5

Answer 1

root5 is the correct answer...

Answer 2

$Given \:\frac{(7+3\sqrt{5})}{3+\sqrt{5}} - \frac{(7-3\sqrt{5})}{3-\sqrt{5}}$

$= \:\frac{(7+3\sqrt{5})(3-\sqrt{5}) - (7-3\sqrt{5})(3+\sqrt{5})}{(3+\sqrt{5})(3-\sqrt{5})}$

$= \frac{21-7\sqrt{5}+9\sqrt{5} - 15 - (21+7\sqrt{5}-9\sqrt{5} - 15)}{3^{2} - (\sqrt{5})^{2}}$

$= \frac{21+2\sqrt{5} - 15 - (21-2\sqrt{5} - 15)}{9 - 5}$

$= \frac{21+2\sqrt{5} - 15 - 21+2\sqrt{5} + 15}{4}$

$= \frac{2\sqrt{5} +2\sqrt{5}}{4}$

$= \frac{4\sqrt{5}}{4}$

$= \sqrt{5}$

Therefore.,

$\red {\frac{(7+3\sqrt{5})}{3+\sqrt{5}} - \frac{(7-3\sqrt{5})}{3-\sqrt{5}}}\green{ = \sqrt{5} }$

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