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The expression is:

$$\frac{4\surd3 + 5\surd2}{\surd48 + \surd18}$$

and its simplification is:

$$\frac{3}{5} + \frac{4\surd6}{15}$$

How can I perform such simplification in Mathematica?

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    $\begingroup$ Try RootReduce in combination with Expand. Next time please have in mind to write your code in the Mathematica form, to enable the easy copy/pasting it. $\endgroup$ – Alexei Boulbitch Dec 5 '18 at 12:21
  • $\begingroup$ @AlexeiBoulbitch Using Expand[RootReduce[ex]], where ex is the expression to be simplified, I obtain 3/5 + (4 Sqrt[2/3])/5, which is not the same as the target expression. By the way, FullSimplify[ex] yields 1/15 (9 + 4 Sqrt[6]), which is simpler (as measured by LeafCount) than the target expression. $\endgroup$ – bbgodfrey Dec 5 '18 at 12:27
  • $\begingroup$ @bbgodfrey Yes, so did I. However, the transformation from 3/5 + (4 Sqrt[2/3])/5 to the desired form is obvious, and the OP did not even give the copy-pastable expression. Therefore, I limited myself by a mere advice. $\endgroup$ – Alexei Boulbitch Dec 5 '18 at 12:42
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(4 Sqrt[3] + 5 Sqrt[2])/(Sqrt[48] + Sqrt[18]) // FullSimplify

Out= $\frac{1}{15} \left(4 \sqrt{6}+9\right)$

or

(4 Sqrt[3] + 5 Sqrt[2])/(Sqrt[48] + Sqrt[18]) // FullSimplify // Expand

Out = $ \frac{4 \sqrt{\frac{2}{3}}}{5}+\frac{3}{5}$

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