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Math Help - Rewrite expression with a rational denominator

  1. #1
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    Rewrite expression with a rational denominator

    \frac{\sqrt{5}-1}{\sqrt{5}+3} Rewrite the expression with a rational denominator

    I start by multiplying top and bottom by \sqrt{5}-3

    =\frac{(\sqrt{5}-1)(\sqrt{5}-3)}{(\sqrt{5}+3)(\sqrt{5}-3)}

    Is my next step correct please?

    =\frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}
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  2. #2
    Member rowe's Avatar
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    Yeah, keep simplifying.

    \frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}

    =\frac{8-4\sqrt{5}}{-4}

    =-(2-\sqrt{5})

    =\sqrt{5}-2
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  3. #3
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    Quote Originally Posted by rowe View Post
    Yeah, keep simplifying.

    \frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}

    =\frac{8-4\sqrt{5}}{-4}

    =-(2-\sqrt{5})

    =\sqrt{5}-2
    Thanks, I was not sure what to do with the -4 denominator, this is a big help.

    However, I'm still confused because the answer given on the worksheet is -\frac{(1+\sqrt{5})}{2}
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  4. #4
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    Smile

    the answer should be \sqrt{5}-2,probably there were a typo on your worksheet.
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  5. #5
    Member rowe's Avatar
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    Quote Originally Posted by Meggomumsie View Post
    Thanks, I was not sure what to do with the -4 denominator, this is a big help.

    However, I'm still confused because the answer given on the worksheet is -\frac{(1+\sqrt{5})}{2}
    Look at the original expression. We know \sqrt{5} > 1, but the worksheet answer gives a negative number. I'm sure there's been a mistake.
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