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anonymous

  • one year ago

Help needed again? Rationalize the denominator and simplify.

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  1. anonymous
    • one year ago
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    \[\frac{ 2\sqrt{x}-3\sqrt{y} }{ \sqrt{x}+\sqrt{y} }\]

  2. Owlcoffee
    • one year ago
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    You might want to use the conjugate formula: \[\sqrt a - \sqrt b = \frac{ a-b }{ \sqrt a + \sqrt b }\]

  3. anonymous
    • one year ago
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    Well I know the conjugate formula. Its doing the actual math that always seems to ruin the result.

  4. anonymous
    • one year ago
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    I know to multiply it by \[\frac{ \sqrt{x}-\sqrt{y} }{ \sqrt{x}-\sqrt{y} }\]

  5. anonymous
    • one year ago
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    What I am specifically having trouble with is multiplying the numerator.

  6. Owlcoffee
    • one year ago
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    Try forming a square difference.

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

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