Simplifying Rational Expressions

[sascha]

How can I simplify the expression below with the HP Prime? I like to see u^n over v^2 as the result.

[rawi]

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

[robmio]

Try to use, in sequence, "texpand" and then "simplify"

Greetings, Robmio

[sascha]

(07-08-2021 09:38 AM)robmio Wrote:  Try to use, in sequence, "texpand" and then "simplify"

Greetings, Robmio

That's what I get:

   

[robmio]

Hi, you don't have to use "expand", but "texpand", followed by "simplify".

[Albert Chan]

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

[sascha]

(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:
   

[sascha]

(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!

   

[Hlib]

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.

[dah145]

(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.

[Hlib]

Yes, I have edit my mistake.