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Math Help - solving algebraic equations with square roots

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    solving algebraic equations with square roots

    im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x
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    Re: solving algebraic equations with square roots

    Quote Originally Posted by kingsolomonsgrave View Post
    im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x
    Notice that \frac{\sqrt{x}-1}{x-1}=\frac{1}{\sqrt{x} +1}

    So solve \frac{1}{\sqrt{x} +1}=0.25
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    Re: solving algebraic equations with square roots

    thanks! how did you know to rationalize the numerator?
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    Re: solving algebraic equations with square roots

    Quote Originally Posted by kingsolomonsgrave View Post
    thanks! how did you know to rationalize the numerator?
    Years and Years of experience.
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    Re: solving algebraic equations with square roots

    if you have the knack for factoring ...

    \frac{\sqrt{x} - 1}{x - 1} = \frac{\sqrt{x} - 1}{(\sqrt{x} - 1)(\sqrt{x}+1)}
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