# solving algebraic equations with square roots

• May 25th 2012, 06:43 AM
kingsolomonsgrave
solving algebraic equations with square roots
im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x
• May 25th 2012, 07:33 AM
Plato
Re: solving algebraic equations with square roots
Quote:

Originally Posted by kingsolomonsgrave
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 $\frac{1}{\sqrt{x} +1}=0.25$
• May 25th 2012, 07:49 AM
kingsolomonsgrave
Re: solving algebraic equations with square roots
thanks! how did you know to rationalize the numerator?
• May 25th 2012, 07:52 AM
Plato
Re: solving algebraic equations with square roots
Quote:

Originally Posted by kingsolomonsgrave
thanks! how did you know to rationalize the numerator?

Years and Years of experience.
• May 25th 2012, 08:58 AM
skeeter
Re: solving algebraic equations with square roots
if you have the knack for factoring ...

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