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I think it is fairly easy to see that

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

Now given the fraction on the left in Maple, how can we get to the equivalent expression on the right? I apologize in advance, if this is rather obvious. But after trying a few things, I have not been able to make it work.

I have used simplify(1/(sqrt(2)-1) and simplify(1/(sqrt(2)-1) * ((sqrt(2)+1)/(sqrt(2)+1)). In both cases, Maple simply returns the first expression on the left $\frac{1}{\sqrt 2 -1}$.

Josh
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    Don’t know Maple, but this process is usually called “rationalizing the denominator.” – Thomas Andrews Aug 15 '21 at 01:42
  • "rationalizing the denominator" is a general term. Using conjugates is one way to rationalize the denominator. I am not sure if conjugates is a term that is being used often, but that is the one I have been taught. – Josh Aug 15 '21 at 01:51
  • In Mathematica: Simplify[1/(Sqrt[2]-1)] gives the answer. By the way, this question has little to do with math but explicitly refers to a symbol-manipulation program, and hence should be closed or migrated. – David G. Stork Aug 15 '21 at 03:07
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    I’m voting to close this question because this is about a particular software system.... not math per se. – David G. Stork Aug 15 '21 at 03:07

1 Answers1

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Thanks to Thomas, upon looking up rationalizing the denominator, I learnt Maple has a built-in function for this purpose:

rationalize(1/(sqrt(2)-1))

gives what I want. For interested reader, have a look at the documentation page here.

Josh
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