# Math Help - solving algebraic equations with square roots

1. ## solving algebraic equations with square roots

im trying to solve (x^0.5 - 1)/(x-1) = 0.25 for x

2. ## Re: solving algebraic equations with square roots

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 $\frac{1}{\sqrt{x} +1}=0.25$

3. ## Re: solving algebraic equations with square roots

thanks! how did you know to rationalize the numerator?

4. ## Re: solving algebraic equations with square roots

Originally Posted by kingsolomonsgrave
thanks! how did you know to rationalize the numerator?
Years and Years of experience.

5. ## Re: solving algebraic equations with square roots

if you have the knack for factoring ...

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