The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: $\displaystyle\frac{a^2-b^2}{a+b}=a-b$.
$\sqrt{x}-\sqrt{y}$
Final answer to the problem
$\sqrt{x}-\sqrt{y}$
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Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.