Simplify the following radicals by rationalizing the denominators.

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Simplify the following radicals by rationalizing the denominators.

Mathematics
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one sec i am posting it.
\[ \frac{x-y}{\sqrt{x}+\sqrt{y}} \]
\[\frac{x-y}{\sqrt{x}+\sqrt{y}}\]\[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]

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Now multiply those, you will have removed the radical sign from the denominator.
how do i multiply them?
|dw:1328019438214:dw|
Then i simplify? or no?
Actually you don't need to multiply the numerator, \[\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]
So all you have to do is multiply the denominator and that will be the answer?
In all similar problems as this one, just multiply the numerator and the denominator with the conjugate of the denominator, just as I did. And then you need to simplify. But in this problem, one of the terms of the numerator gets cancelled. Did you understand?
Did I puzzle you? Should I write down the whole thing again, in a concise way?
You puzzled me sorry haha :/ I am terrible at math.
Ok, then I am writing down the whole thing in a better way....
You were given with the following expression \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\] right?
Correct.
Now I multiply both the numerator and the denominator with the conjugate of the dimnomnator i.e. \[\sqrt{x}-\sqrt{y}\] So the expression gets converted to \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]
Is it clear till this step? I can multiply something to the numerator and as well as to the denominator since they can be cancelled Is it clear?
Yes it is clear. I just do not know how to multiply correctly?
So now I can say \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]\[=\frac{(x-y)({\sqrt{x}-\sqrt{y}})}{\sqrt{(x)^2}+\sqrt{(y)^2}}\]\[=\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]
so the answer is the last part of that problem?
The answer is \[\sqrt{x}-\sqrt{y}\]
oh sorry didn't mean to put () and that is simpler then it looks i guess i was just over thinking it.
Did you understand?
yes i did thanks!

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