Question

Help needed again?
Rationalize the denominator and simplify.

Answer 1

\[\frac{ 2\sqrt{x}-3\sqrt{y} }{ \sqrt{x}+\sqrt{y} }\]

Answer 2

You might want to use the conjugate formula:
\[\sqrt a - \sqrt b = \frac{ a-b }{ \sqrt a + \sqrt b }\]

Answer 3

Well I know the conjugate formula. Its doing the actual math that always seems to ruin the result.

Answer 4

I know to multiply it by \[\frac{ \sqrt{x}-\sqrt{y} }{ \sqrt{x}-\sqrt{y} }\]

Answer 5

What I am specifically having trouble with is multiplying the numerator.

Answer 6

Try forming a square difference.

Answer 7

\[\frac{ 2\sqrt x - 3 \sqrt y }{\sqrt x +\sqrt y }\frac{ ( \sqrt x - \sqrt y) }{ (\sqrt x - \sqrt y) }\]
\[\frac{ 2x-2\sqrt x \sqrt y -3 \sqrt y \sqrt x +3y }{ x-y }\]
\[\frac{ 2x-5 \sqrt x \sqrt y +3y }{ x-y }\]
This is what you get if you multiply to what you suggested.