Question

3-√5 /3+2√5 Rational​

Answer 1

Let me assume Rational means the expression must be rationalised.

Answer:

$\frac{9 \sqrt{5} - 19}{11}$

Step-by-step explanation:

We have

$\frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } = \frac{(3 - \sqrt{5})(3 - 2 \sqrt{5}) }{(3 + 2 \sqrt{5})(3 - 2 \sqrt{5}) } = \frac{9 - 6 \sqrt{5} - 3 \sqrt{5} + 10}{ {3}^{2} - {(2 \sqrt{5}) }^{2} } = \frac{19 - 9 \sqrt{5} }{9 - 20} = \frac{19 - 9 \sqrt{5} }{ - 11} = \frac{9 \sqrt{5} - 19}{11}$