Question

rationalize 3+√2/3-4√7

Answer 1

Step-by-step explanation:

$= \frac{3 + \sqrt{2} }{3 - 4 \sqrt{7} } \times \frac{3 + 4 \sqrt{7} }{3 + 4 \sqrt{7} } \\ \\ = \frac{9 + 12 \sqrt{7} + 3 \sqrt{2} + 4 \sqrt{14} }{ {3}^{2} - {(4 \sqrt{7} )}^{2} } \\ \\ = \frac{9 + 12 \sqrt{7} + 3 \sqrt{2} + 4 \sqrt{14} }{9 - 112} \\ \\ = \frac{9 + 12 \sqrt{7} + 3 \sqrt{2} + 4 \sqrt{14} }{ - 96 }$