Question

please solve with complete steps.​

Answer 1

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Answer 2

Answer:

$\sqrt{5} - \sqrt{3}$

Explanation:

find LCM and solve

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

$\frac{2+(5-\sqrt{15}+\sqrt{15}-3)}{2(\sqrt{5}+\sqrt{3}) }$

$\frac{2+2}{2(\sqrt{5}+\sqrt{3}) }$

$\frac{4}{2(\sqrt{5}+\sqrt{3}) }$

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

rationalize

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

$\frac{2(\sqrt{5}-\sqrt{3}) }{5-\sqrt{15}+\sqrt{15}-3 }$

$\frac{2(\sqrt{5}-\sqrt{3}) }{2}$

$=\sqrt{5}-\sqrt{3}$