Question

How do i simplify this.

(-y+√(xy))/(√(x)-√(y))

Answer 1

ratinalize the denominator

Answer 2

I sometimes find it easier to not look at all of the radicals until later. if you let \(a = \sqrt{x}\) and \(b = \sqrt{y}\) you could rewrite it as \[\frac{-y+\sqrt{xy}}{\sqrt{x}-\sqrt{y}} = \frac{-b^2+ab}{a-b}\] and grind away, then substitute back at the end. Just looking at it in that form you might see a first step that is easier than rationalizing the denominator...