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

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2 Answers

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
is that the entire question?? what's the context?
you can't really do much what i can think of is rationalize the denominator