Simplifying Rational Expressions

[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