I'm doing some work on functions and have come across a problem in which I need to simplify a certain expression. I can't move any further on because I'm unsure of how to simplify this expression!

Here it is: $$ \frac{1}{\sqrt{1+\sqrt{x^2-1}}} $$

Any help is appreciated, thanks so much!


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  • $\begingroup$ Do you mean $\frac{1}{\sqrt{1 + \sqrt{x^2 - 1}}}$? $\endgroup$ – N. F. Taussig Apr 4 '17 at 14:24
  • 1
    $\begingroup$ Wasn't this question asked 30 minutes ago? $\endgroup$ – kingW3 Apr 4 '17 at 14:25
  • $\begingroup$ @N.F.Taussig Yes! Thank you $\endgroup$ – CalcStdntD Apr 4 '17 at 14:25
  • $\begingroup$ Here is a tutorial on how to typeset mathematics on this site. $\endgroup$ – N. F. Taussig Apr 4 '17 at 14:27
  • $\begingroup$ @N.F.Taussig That's great, thanks! $\endgroup$ – CalcStdntD Apr 4 '17 at 14:29

I don't think there is much that can be done. If you want to avoid the "square root inside square root", you can expand the fraction with $\sqrt{1-\sqrt{x^2-1}}$ or $\sqrt{\sqrt{x^2-1} - 1}$, depending on which version produces a positive discriminant:

$$ \frac{1}{\sqrt{1+\sqrt{x^2-1}}} = \frac{\sqrt{1-\sqrt{x^2-1}}}{\sqrt{2-x^2}} $$


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