Question 167075
Let sqrt = square root

sqrt{6}/(sqrt{5} - sqrt{3})

Multiply the top and bottom by [sqrt{5} + sqrt{3}]

sqrt{6} times sqrt{5} + sqrt{3} = sqrt{30} + sqrt{18}...Our numerator

[sqrt{5} - sqrt{3}] times [sqrt{5} + sqrt{3}] = sqrt{25} - sqrt{9}...our denominator

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We now have the following fraction:

[sqrt{30} + sqrt{18}]/[sqrt{25} - sqrt{9}]

In the denominator, we have two perfect squares.

So, sqrt{25} = 5 and sqrt{9} = 3

Then 5 - 3 = 2.

In the numerator, sqrt{30} is already in lowest terms and so it stays the same.
However, sqrt{18} becomes 3(sqrt{2}).

Final answer:  [3(sqrt{2}) + sqrt{30}]/2