 Rationalizing a denominator - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Rationalizing a denominator (/thread-14736.html) Rationalizing a denominator - rrpalma - 03-29-2020 03:40 AM 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! RE: Rationalizing a denominator - parisse - 03-30-2020 12:21 PM 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))/(y-sqrt(2))), that does not happen if there is only one sqrt. normal does not do this (and mult_conjugate is even more precise).