Question

Someone plz solve this question​

Answer 1

√5

Step-by-step explanation:

This is a like fraction. We don't need to rationalize , Just simplify .

Note

Like Fraction : When the denominator of two fraction are same but different in sign .

Solution:

$\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } \\ \\ \frac{(7 + 3 \sqrt{5} )(3 - \sqrt{5} ) - (7 - 3 \sqrt{5} )(3 + \sqrt{5}) }{(3 + \sqrt{5})(3 - \sqrt{5} ) } \\ \\ \frac{(21 - 7 \sqrt{5} + 9 \sqrt{5} - 3.5) - (21 + 7 \sqrt{5} - 9 \sqrt{5} - 3.5)}{(3 + \sqrt{5})( 3 - \sqrt{5} )} \\ \\ \frac{(21 + 2 \sqrt{5} - 15) - (21 -2 \sqrt{5} - 15)}{ {3}^{2} - {( \sqrt{5}) }^{2} } \\ \\ \frac{21 - 15 + 2 \sqrt{5} - 21 + 15 + 2 \sqrt{5} }{9 - 5} \\ \\ \frac{4 \sqrt{5} }{4} \\ \\ \sqrt{5} \:$

Hence the required answer is √5 .