For all x > 0 and y > 0, the radical expression

(√x)÷(3√x-√y)s equivalent to:

For all x > 0 and y > 0, the radical expression

(√x)÷(3√x-√y)s equivalent to:

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Katy, TX

Now, this is a weird question, because the answer is more complicated to evaluate than the original question. However, it appears they want you to rationalize the denominator.

sqrt(x)

----------

3*sqrt(x) - sqrt(y)

Multiply top and bottom by the **conjugate**:

x^{1/2}(3x^{1/2} + y^{1/2})

----------------------

(3x^{1/2} - y^{1/2})(3x^{1/2} + y^{1/2})

3x + x^{1/2}y^{1/2}

-----------------

9x + 3x^{1/2}y^{1/2} - 3x^{1/2}y^{1/2} - y

−−−−−−−−−−−−

Let's try it out for x = 16 and y = 9

Original:

16^(1/2)

-----------

3(4) - 3

4/9

New:

3(16) + 16^(1/2) 9^(1/2)

----------------------

9(16) - 9

----------------------

9(16) - 9

48 + (4)(3)

------------

144 - 9

60/135 = 4/9

Minneapolis, MN

is that the entire question?? what's the context?

you can't really do much what i can think of is rationalize the denominator

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