Can this be solved with any HP CAS?

[Nigel (UK)]

(09-29-2017 06:44 PM)SlideRule Wrote:  ...
OK, then expand the equation, collect terms & then simplify.

3x+(1/(x-5)) = 15+(1/(x-5))
expands to
3x² - 15x + 1 = 15x - 75 + 1
collect terms
...
BEST!
SlideRule

The problem is that the second equation above is only equivalent to the original equation when \(x\neq5\), because going from the second equation to the original equation requires division by \((x-5)\) and when \(x=5\) this isn't allowed. Because of this a solution to the second equation may not be a solution to the first equation.

Disclaimer: I am not a mathematician! This is just my understanding of the situation.

Nigel (UK)