im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x
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Originally Posted by kingsolomonsgrave im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x Notice that $\displaystyle \frac{\sqrt{x}-1}{x-1}=\frac{1}{\sqrt{x} +1}$ So solve $\displaystyle \frac{1}{\sqrt{x} +1}=0.25$
thanks! how did you know to rationalize the numerator?
Originally Posted by kingsolomonsgrave thanks! how did you know to rationalize the numerator? Years and Years of experience.
if you have the knack for factoring ... $\displaystyle \frac{\sqrt{x} - 1}{x - 1} = \frac{\sqrt{x} - 1}{(\sqrt{x} - 1)(\sqrt{x}+1)}$
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