Properties of Exponents Issue w/ HP Prime

[Han]

(12-12-2014 06:04 AM)Joe7248 Wrote:  I might be doing it wrong forgive me but I used collect and entered x^(-1/2) and the calculator still returned x^(1/2)/x.

Have you updated to the most recent firmware? What are your CAS settings? Did you make sure to put CAS settings on Minimum? Also, my calculator uses the \( \sqrt{} \) symbol whereas you are suggesting it returns a fractional exponent.

Quote:Here's another concern with this issue... I used the TI-89 Titanium and Wolfram Alpha to get the derivative of: (4 sqrt(x))/(x^2-2)) and the answer equaled -(2 (3 x^2+2))/(sqrt(x) (x^2-2)^2) on both which was great. If needed here is the Wolfram Alpha Language Plain Text Input: D[(4 Sqrt[x])/(x^2-2), x] to see the problem in textbook format. However, the HP Prime provides this as an answer to (4x^(1/2))/(x^2-2)) using the differentiate (diff) option & Maximum Simplify setting (-6x^2*sqrt(x)-4*sqrt(x))/(x^5-4*x^3+4*x) it can also be copied and pasted to Wolfram Alpha to see its textbook format and understand my problem. HP Programmers please correct this its my belief that the answers which have appeared on my HP Prime Calculator, should only appear if Simplify is set to Minimum because the answers can be simplified further. No Excuses! Your answers should not end halfway simplified under Maximum settings. I have faith in your abilities to address this issue and satisfy my concern.

Are you suggesting that \[ \frac{-6x^2\sqrt{x}-4\sqrt{x}}{x^5-4x^3+4x} \] can be simplified more? In what sense of "simplify"? I don't see how you can simplify this more except to possibly multiply the \( x^2 \sqrt{x} \) into a single power of x. The expression
\[ -\frac{2 (3 x^2+2)}{\sqrt{x} (x^2-2)^2} \]
is not simplified because there are multiplication operations that have not been evaluated. I'm only being half-serious here. My point is that "to simplify" in mathematics does not always mean the same thing to everyone.

Using minimum simplification and collect on the result gives the same fraction as the ti89 and wolfram alpha on my machine.


   


Edit: Consider \( (x-b)^2 - (a+x)^2 = -(a+b) (2x+a-b) = -2(a+b)x + (b^2-a^2) \). All three forms are arguably in simplest form depending on what you plan to do with the expression. The first expression collects everything in terms of a and b separately, the second form is nice for finding the zeros of the expression, and the last form is useful if you want to simplify into a polynomial.