x^2 +1 +1/k if I move the k to the right hand of  the = sign first it can't be zero because k/0.

x^2 +1 +1/k if I move the +1 to the right hand of  the = sign first it can't be 1 because that would make 0.
 

So what is it 0 or 1?

 

I probably just made a simple math mistake I apologize if this is a stupid question.

 

 

Edited October 27, 20205 yr by can't_think_of_a_name

I think you're confusing what equation (problem) you actually have, and what values of \( k \) make sense for your problem.

You also seem to have some confusion about what values of \( k \) are valid for your problem.

In your OP, you're proposing up to four different equations:

\[x^{2}+1-1/k=0\]

\[x^{2}+1-1/k=1\]

\[x^{2}+1+1/k=0\]

\[x^{2}+1+1/k=1\]

So the first question I would ask you is: Which one is it? Maybe you want to solve all of them.

The question about what values of \( k \) make sense is simpler. Only those with \( k\neq0 \) make sense for the equations you've written. Moving something or other to the right hand side has nothing to do with it, unless you do it multiplicatively. For example, if your equation were,

\[k\left(x^{2}-k\right)=1\]

you would have to be careful not to divide by \( k \) in case that parameter were \( 0 \).

In general, when you have both unknowns (the thing you want to solve for) and parameters (which define an infinite family of possible equations, one for each possible value of the parameter), you must discuss the equation for every possible value of the parameter. And you must leave out those values of the parameter that don't give a sensible equation.

I hope that helps.