for all x>0 and y>0, the radical expression
√x
3√x - √y

is equivalent to :

3x - √y
9x + y

3x - √xy
3x + y

3x + √xy
9x - y

3x + √xy
3x - y

x
3x - y

those are spost to be fractions didn't know how to do that

for all x>0 and y>0, the radical expression
√x
3√x - √y

is equivalent to :

3x - √y
9x + y

3x - √xy
3x + y

3x + √xy
9x - y

3x + √xy
3x - y

x
3x - y

those are supposed to be fractions didn't know how to do that


\Large \frac {\sqrt{x}}{3\sqrt{x} - sqrt{y}}

Multiply top and bottom by \Large 3\sqrt{x}+sqrt{y}. The reason I picked that is a^2-b^2=(a-b)(a+b). I'm trying to get roots out of the denominator.

\Large \left( \frac {\sqrt{x}}{3\sqrt{x} - sqrt{y}} \right) \left(\frac {3\sqrt{x}+\sqrt{y}}{3\sqrt{x}+\sqrt{y}}\right) = \frac {3x+\sqrt {xy}}{9x-y}

I think this is one of your choices.