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+--- Thread: Simplifying Rational Expressions (/thread-17226.html)
Simplifying Rational Expressions - sascha - 07-08-2021 08:28 AM
How can I simplify the expression below with the HP Prime? I like to see u^n over v^2 as the result.
![[Image: large?v=v2&px=999]](https://h30434.www3.hp.com/t5/image/serverpage/image-id/288197i9089287A4DB32A65/image-size/large?v=v2&px=999)
RE: Simplifying Rational Expressions - rawi - 07-08-2021 09:18 AM
If I make
simplify((u^(n+1)*v^(n+1))/(u*v^(n+3)))
I get a little bit further to u^(n+1)/(u*v^2), but it is not able to reduce the fraction to u^n/v^2. If I try to simplify the exptression u^(n+1)/(u*v^2) I get what you already got.
BTW: If I try expand(((u*v)^(n+1))/(u*v^(n+3))) with the TI89 Titanium I get (u*v)^n/v^(n+2).
If I do expand((u^(n+1)*v^(n+1))/(u*v^(n+3))) I get u^n/v^2.
So this is not perfect but better than the Prime.
Result with TI nspire CX II-T CAS:
expand(((u*v)^(n+1))/(u*v^(n+3))) --> (u*v)^n/(u*v^(n+3))
expand((u^(n+1)*v^(n+1))/(u*v^(n+3))) --> u^n/v^2
So it seams that the brackets in the numerator make things more difficult.
It's really strange because it is mathematically so simple.
Best
Raimund
RE: Simplifying Rational Expressions - robmio - 07-08-2021 09:38 AM
Try to use, in sequence, "texpand" and then "simplify"
Greetings, Robmio
RE: Simplifying Rational Expressions - sascha - 07-08-2021 09:58 AM
(07-08-2021 09:38 AM)robmio Wrote: Try to use, in sequence, "texpand" and then "simplify"
Greetings, Robmio
That's what I get:
[attachment=9625]
RE: Simplifying Rational Expressions - robmio - 07-08-2021 10:26 AM
Hi, you don't have to use "expand", but "texpand", followed by "simplify".
RE: Simplifying Rational Expressions - Albert Chan - 07-08-2021 11:59 AM
CAS> simplify(pow2exp((u*v)^(n+1)/(u*v^(n+3)))) → u^n/v^2
CAS> simplify(pow2exp(u^(n+1)*v^(n+1)/(u*v^(n+3)))) → u^n/v^2
RE: Simplifying Rational Expressions - sascha - 07-08-2021 12:18 PM
(07-08-2021 10:26 AM)robmio Wrote: Hi, you don't have to use "expand", but "texpand", followed by "simplify".
Thanks! Amazing, this works:
[attachment=9627]
RE: Simplifying Rational Expressions - sascha - 07-08-2021 12:23 PM
(07-08-2021 11:59 AM)Albert Chan Wrote: CAS> simplify(pow2exp((u*v)^(n+1)/(u*v^(n+3)))) → u^n/v^2
CAS> simplify(pow2exp(u^(n+1)*v^(n+1)/(u*v^(n+3)))) → u^n/v^2
This works great. Thanks!
[attachment=9628]
RE: Simplifying Rational Expressions - Hlib - 07-09-2021 03:11 PM
My afx-2.0 calculator outputs:
simplify ((U×V)^(N+1)/((U×V)^(N+3)))
result is 1/(U^2×V^2)
Is this correct?
EDIT
My input mistake:
(u×v)^(n+1)/(u×v^(n+3))
Yes, Prime wins.
RE: Simplifying Rational Expressions - dah145 - 07-09-2021 07:07 PM
(07-09-2021 03:11 PM)Hlib Wrote: My afx-2.0 calculator outputs:
simplify ((U×V)^(N+1)/((U×V)^(N+3)))
result is 1/(U^2×V^2)
Is this correct?
The original expression is ((U*V)^(N+1))/(U*(V^(N+3)), my algebra FX 2.0 isn't able to simplify it.
RE: Simplifying Rational Expressions - Hlib - 07-09-2021 07:27 PM
Yes, I have edit my mistake.