Multiply the radicals: √(x/y-y/x)1/xy * √x+y/x-y Show solution and make sure that everything is in its simplest form.

Expert Answers

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You need to bring the terms `x/y - y/x ` to a common denominator such that:

`((x^2 - y^2)/(xy))*(1/(xy)) = (x^2 - y^2)/(x^2y^2)`

You need to substitute the special product `(x-y)(x+y)`  for `x^2 - y^2`  such that:

`((x-y)(x+y) )/(x^2y^2)`

You need to multiply`((x-y)(x+y) )/(x^2y^2) by (x+y)/(x-y)`  such that:

`((x-y)(x+y) )/(x^2y^2)*(x+y)/(x-y) = ((x+y)^2)/(x^2y^2)`

You need to evaluate the square root of the fraction such that:

`sqrt (((x+y)^2)/(x^2y^2)) = |(x+y)/(xy)|`

Hence, multiplying the square roots yields `sqrt((x/y - y/x)*(1/(xy)))*sqrt ((x+y)/(x-y)) = |(x+y)/(xy)|.`

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