we are given with the expression to simplify
[tex] \sqrt{2} +\frac{1}{\sqrt{2}} [/tex]
This can be simplified as below
[tex] \sqrt{2} +\frac{1}{\sqrt{2}}=\sqrt{2} +\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}} \\
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on \ simplification \ we \ get\\
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\sqrt{2} +\frac{1}{\sqrt{2}}=\sqrt{2} +\frac{\sqrt{2}}{2} \\
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Now \ add \ the \ terms \ on \ right \ side\\
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\sqrt{2} +\frac{1}{\sqrt{2}}=\frac{2\sqrt{2}+\sqrt{2}}{2} \\
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Simplify\\
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\sqrt{2} +\frac{1}{\sqrt{2}}=\frac{3\sqrt{2}}{2} \\
\\ [/tex]
