Question

Simplify the following by rationalizing the denominator.

7+3√5 / 7-3√5

Answer 1

see the picture

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Answer 2

Step-by-step explanation:

$\frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \frac{(7) {}^{2}{ + } (3 \sqrt{5} ) {}^{2} \: + 2(7)(3 \sqrt{5)} }{(7) {}^{2} - (3 \sqrt{5}) {}^{2} } \\ \frac{49 + 45 + 42 \sqrt{5} }{49 - 45} \\ \frac{94 + 42 \sqrt{5} }{4} \\ \frac{47 + 21 \sqrt{5} }{2}$