Taking the limit as x approaches infinity of: $\displaystyle \frac{x^2}{x-1}-\frac{x^2}{x+1}$ can be rewritten as:

The limit as x approaches infinity of: $\displaystyle \frac{x^2}{x-1}$ MINUS the limit as x approaches infinity of: $\displaystyle \frac{x^2}{x+1}$

But this isn't true.

If I re-arrange algebraically in the first example, I will get x=2.

However, if I solve the rewritten problem, I get infinity minus infinity or undefined...??