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**[SOLVED] Why eliminate answers?**

In my book, Essential Calculus, a section is introduced with limits. They introduce a random(maybe) function :

[tex]Q(h) = \frac {2h + h^2}{h} (h \neq 0)[/tex]

"We then divide the numerator by the denominator h, which is permissible since [tex]h \neq 0[/tex]. This gives the simple formula [tex]Q(h) = 2 + h (h \neq 0)[/tex]"

I was always told you do not divide by variables like in a trigonometric equation because it eliminates solutions. How are they then to say that it is permissible since [tex]h \neq 0[/tex] ? I don't understand.