Rationalizing a denominator
03-29-2020, 03:40 AM (This post was last modified: 03-29-2020 03:55 AM by rrpalma.)
Post: #1
 rrpalma Junior Member Posts: 29 Joined: Aug 2014
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.

03-30-2020, 12:21 PM
Post: #2
 parisse Senior Member Posts: 1,242 Joined: Dec 2013
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))/(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).
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)