Question

simplify 2+3root5 divided by 2-3root5

Answer 1

$\frac{2 + 3 \sqrt{5} }{2 - 3 \sqrt{5} }$


By rationalization,


$\frac{2 + 3 \sqrt{5} }{2 - 3 \sqrt{5} } \times \frac{2 + 3 \sqrt{5} }{2 + 3 \sqrt{5} } \\ \\ \frac{ {(2 + 3 \sqrt{5}) }^{2} }{( {2})^{2} - {(3 \sqrt{5} )}^{2} } \\ \\ \frac{4 + 45 + 12 \sqrt{5} }{4 - 45} \\ \\ \frac{49 + 12 \sqrt{5} }{ - 41} \\ \\ - \frac{49 + 12 \sqrt{5} }{41}$




I hope this will help you


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