Why is this not 0 on 50g or Prime?

[ijabbott]

(07-16-2018 03:35 PM)Joe Horn Wrote:  \[\frac { 1 }{ \infty +\cfrac { 1 }{ 0 } } =\frac { 1 }{ \infty +\infty } =\frac { 1 }{ \infty } =0\]The above is correct, no? Why then do both the HP 50g (in exact mode) and the HP Prime (in CAS view) say that the first expression, 1/(inf+1/0), is "undefined"?

Because \( \frac{1}{0} \) is undefined? Or failing that, because \( \infty + \frac{1}{0} = \frac{\infty \cdot 0 + 1}{0} \) and \(\infty \cdot 0\) is undefined?