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

Question

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

(√x)÷(3√x-√y)s equivalent to:

Answer 1

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^1/2y^1/2

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

9x + 3x^1/2y^1/2 - 3x^1/2y^1/2 - y

 

 

    3x + x^1/2y^1/2

−−−−−−−−−−−−

        9x - 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

 

48 + (4)(3)

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

144 - 9

 

60/135 = 4/9

Answer 2

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

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