solving algebraic equations with square roots

**kingsolomonsgrave** · May 25th 2012, 05:43 AM

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

**Plato** · May 25th 2012, 06:33 AM

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

**kingsolomonsgrave** · May 25th 2012, 06:49 AM

thanks! how did you know to rationalize the numerator?

**Plato** · May 25th 2012, 06:52 AM

Originally Posted by kingsolomonsgrave

thanks! how did you know to rationalize the numerator?

Years and Years of experience.

**skeeter** · May 25th 2012, 07:58 AM

if you have the knack for factoring ...

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

Thread: solving algebraic equations with square roots