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# ​Write the sum in as a single rational expression:

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Write the sum in as a single rational expression:

Guest Nov 4, 2017
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We need to get a common denominator. Let's multiply the first fraction by  3/3 .

$$\frac{\sqrt5}{10}+\frac{\sqrt2}{6}+2 \\~\\ =\,\frac{\sqrt5}{10}\cdot\frac33+\frac{\sqrt2}{6}+2 \\~\\ =\,\frac{3\sqrt5}{30}+\frac{\sqrt2}{6}+2$$

Now let's multiply the second fraction by  5/5 .

$$=\,\frac{3\sqrt5}{30}+\frac{5\sqrt2}{30}+2$$

And multiply the  2  by  30/30 .

$$=\,\frac{3\sqrt5}{30}+\frac{5\sqrt2}{30}+\frac{60}{30}$$

Now we can add the fractions together.

$$=\,\frac{3\sqrt5+5\sqrt2+60}{30}$$

hectictar  Nov 4, 2017