-5
$\begingroup$

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!

$\endgroup$

closed as off-topic by Lord_Farin, KReiser, José Carlos Santos, Cesareo, metamorphy Jan 11 at 11:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, KReiser, José Carlos Santos, Cesareo, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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
0
$\begingroup$

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:

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

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.