Question

Can u answer this question?

Answer 1

Answer:

if the question is an objective question

Answer 2

Answer: √5-√3

Step-by-step explanation:

$\displaystyle\\\frac{1}{\sqrt{5}+\sqrt{3} } +\frac{1}{2} (\sqrt{5} -\sqrt{3})$

Let us reduce this expression to a common denominator:

$\displaystyle\\\frac{1+\frac{1}{2}(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3}) }{\sqrt{5} +\sqrt{3} } =\\\\\frac{1+\frac{1}{2}((\sqrt5)^2 -(\sqrt{3} )^2) }{\sqrt{5}+\sqrt{3} } =\\\\\frac{1+\frac{1}{2}(5-3) }{\sqrt{5} +\sqrt{3} } =\\\\\frac{1+\frac{1*2}{2} }{\sqrt{5} +\sqrt{3}} =\\\\\frac{1+1}{\sqrt{5} +\sqrt{3} } =\\\\\frac{2}{\sqrt{5}+\sqrt{3} }$

Let's get rid of the irrationality in the denominator:

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