anonymous one year ago Help needed again? Rationalize the denominator and simplify.

1. anonymous

$\frac{ 2\sqrt{x}-3\sqrt{y} }{ \sqrt{x}+\sqrt{y} }$

2. Owlcoffee

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. Owlcoffee

Try forming a square difference.

7. Owlcoffee

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