anonymous
  • anonymous
Help needed again? Rationalize the denominator and simplify.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ 2\sqrt{x}-3\sqrt{y} }{ \sqrt{x}+\sqrt{y} }\]
Owlcoffee
  • Owlcoffee
You might want to use the conjugate formula: \[\sqrt a - \sqrt b = \frac{ a-b }{ \sqrt a + \sqrt b }\]
anonymous
  • anonymous
Well I know the conjugate formula. Its doing the actual math that always seems to ruin the result.

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anonymous
  • anonymous
I know to multiply it by \[\frac{ \sqrt{x}-\sqrt{y} }{ \sqrt{x}-\sqrt{y} }\]
anonymous
  • anonymous
What I am specifically having trouble with is multiplying the numerator.
Owlcoffee
  • Owlcoffee
Try forming a square difference.
Owlcoffee
  • 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.

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