Question

7+3 root 5 / 3+root 5 - 7-3root5 /3-root5

Answer 1

Please refer to the above photo for the used process

Hope this will be helping you

Answer 2

Answer:

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

Explanation:

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

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

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

= $\frac{21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15}{9-5}$

=$\frac{(-14\sqrt{5}+18\sqrt{5})}{4}$

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

= $\sqrt5$

Therefore,

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

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