I'm working through some rationalization problems and came across this problem:


The answer is given as:


I can't for the life of me figure out how to get there. Pretty sure I'm supposed to multiply $\frac{1}{\sqrt{x}}-1$ by its conjugate radical $\frac{1}{\sqrt{x}}+1$, but I still can't get to their answer.

A step-by-step rationalization would be much appreciated!



  • $\begingroup$ Man, it was that first step (multiplying top and bottom by $\sqrt{x}$ that I missed. ...getting back into math and teaching myself precalc/calc again. One step at a time! $\endgroup$ – Joel Brewer Jul 24 '16 at 3:06

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


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