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

For all x > 0 and y > 0, the radical expression
(√x)÷(3√x-√y)s equivalent to:

### 2 Answers by Expert Tutors

Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
0
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:

x1/2(3x1/2 + y1/2)
----------------------
(3x1/2 - y1/2)(3x1/2 + y1/2)

3x + x1/2y1/2
-----------------
9x + 3x1/2y1/2 - 3x1/2y1/2 - y

3x + x1/2y1/2
−−−−−−−−−−−−
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
Samir Z. | Experienced calculus tutorExperienced calculus tutor
4.5 4.5 (2 lesson ratings) (2)
-1
is that the entire question?? what's the context?
you can't really do much what i can think of is rationalize the denominator