Extraneous and missing solutions

[Mentallic]

While solving equations, most would have at some point or another had to deal with the annoyance of extraneous or missing solutions.
While I have vigorously taught myself over the years how to avoid losing solutions, gaining extra solutions is still and will probably always be inevitable for me (in order to keep things simple).

I'm curious to know if extraneous solutions can be found and eliminated in a set of solutions by means other than substituting and checking in the original equation.

 

[symbolipoint]

Mentallic, the best way is to examine the original equation or origianal set of equations. Examine those for values which will not work or need to be excluded. Is your viewpoint that of intermediate algebra and Pre-Calculus?

 

[Mentallic]

I agree examining the equation would also suffice, but this is sometimes not so obvious, which would again lead to simple plug-and-check.

Yes my viewpoint is just that, but does this mean the rules don't apply so bluntly for post-calculus mathematics?