Question

tell the answer with steps​

Answer 1

Answer:

$\frac{32+2\sqrt{15}}{{13}}$

Step-by-step explanation:

$\frac{4+\sqrt{5} }{4-\sqrt{3} }$ + $\frac{4-\sqrt{5} }{4+\sqrt{3} }$

= $\frac{(4+\sqrt{5})\times(4+\sqrt{3}) + (4-\sqrt{5})\times(4-\sqrt{3}) }{(4-\sqrt{3})*(4+\sqrt{3}) }$

= $\frac{(4^2+4(\sqrt{3}+\sqrt{5})+\sqrt{3}*\sqrt{5} ) + (4^2-4(\sqrt{3}+\sqrt{5})+\sqrt{3}*\sqrt{5} )}{{(4-\sqrt{3})*(4+\sqrt{3}) }}$

= $\frac{(16+4\sqrt{3}+4\sqrt{5}+\sqrt{15} ) + (16-4\sqrt{3}-4\sqrt{5})+\sqrt{15} )}{{(4^2 -\sqrt{3}^2)}}$

= $\frac{16+16+\sqrt{15} +\sqrt{15} )}{{(16 -3)}}$

= $\frac{32+2\sqrt{15}}{{13}}$

Answer 2

Step-by-step explanation:

Hope it helps to you all.