Simplify symbolic equations based in assumptions

[Nick11014]

I am trying to simplify a symbolic equation like ( x * y ) / ( x + y ) using the assume() function.

If y is much greater than x, then:
x + y = y;
( x * y ) / ( x + y ) = ( x * y ) / ( y ) = x

What i tried to do is something like

Code:


assume(y >> x ); // >> does not work. just for exemplification
simplify(( x * y ) / ( x + y )); // returns x

Is this possible ?

[C.Ret]

(06-26-2024 03:26 PM)Nick11014 Wrote:  If y is much greater than x, then: x + y = y; ( x * y ) / ( x + y ) = ( x * y ) / ( y ) = x

Bonsoir,

When \( y \) is very large in front of \(x\), there is no real equality. One way to see things is to consider the asymptote form: \( \displaystyle \lim_{ x \ll y}\left(\frac{x\cdot y}{x+y}\right) = x \).

To obtain such a result on the HP Prime, one way is to use an extra CAS variable to symbolized the ratio \( r = \frac{x}{y}\). Having \( x \ll y \) is equivalent to have \(r\) approaching zero :
\( \displaystyle \lim_{ x \ll y}\left(\frac{x\cdot y}{x+y}\right) = \displaystyle \lim_{ r \to 0}\left(\frac{x\cdot y}{x+y}\right) = x \) where \( r = \frac{x}{y}\).