Rationalizing a denominator

03292020, 03:40 AM
(This post was last modified: 03292020 03:55 AM by rrpalma.)
Post: #1




Rationalizing a denominator
Hello,
I'm in the process of rekindling my love for the Prime. I just ran into the following with the CAS: If I have the expression (SQRT(x) + 2) / (SQRT(x)  2) and use the simplify() function, I do get a rational expression that eliminates the radicand in the denominator. However, if I replace 2 with SQRT(2), both on the numerator and the denominator ie, I enter (SQRT(x) + SQRT(2)) / (SQRT(x)  SQRT(2)) and the invoke the simplify() function, I obtain : (SQRT(2)  SQRT(x)) / (SQRT(2)  SQRT(x)) ie, the calculator multiplies both the numerator and the denominator by 1, but it doesn't eliminate the radicands in the denominator. In order to get my expected result, I need to use the mult_conjugate() function, followed by expand() and then collect() Any idea why this happens? I am using the HP Prime Emulator on MacOS. Thanks for reading! 

03302020, 12:21 PM
Post: #2




RE: Rationalizing a denominator
It's very hard to find good rules to implement simplify. simplify does a temporary replacement of sqrt(x) with a free identifier (like if you simplify (y+sqrt(2))/(ysqrt(2))), that does not happen if there is only one sqrt.
normal does not do this (and mult_conjugate is even more precise). 

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