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√338      √ 150

____  +  _____    =

√288         √96

13√2         5√6

____  +    ____   =

12√2         4√6

13             5

__    +      __   =

12             4

13         15

__  +     ___     =

12         12

28

__    =

12

7

__

3

Hi Guest, 

First, 

$\frac{\sqrt{338}}{\sqrt{288}}+\frac{\sqrt{150}}{\sqrt{96}} = \frac{13}{2^2\cdot \:3}+\frac{\sqrt{150}}{\sqrt{96}}$

Next, $\frac{13}{2^2\cdot \:3}+\frac{\sqrt{150}}{\sqrt{96}} = \frac{13}{2^2\cdot \:3}+\frac{5}{2^2}$

Simplifying again, $\frac{13}{2^2\cdot \:3}+\frac{5}{2^2} = \frac{13}{12}+\frac{5}{2^2}$

Lastly, $\frac{13}{12}+\frac{5}{2^2} = \frac{13}{12} + \frac{5}{4} = \frac{13}{12}+\frac{15}{12} = \frac{28}{12} = \frac{7}{3}$

Your welcome :P, Evan

Oops CPhill was more detailed Sorry!