I have f(x) = (x^2+x-2)/(x-1) and g(x) = x+2(adsbygoogle = window.adsbygoogle || []).push({});

Now everyone would agree that f has a domain R\{1} and g has a domain R.

Yet I can write (x^2+x-2)/(x-1) = x+2

So why wouldn't g have a domain R\{1} if I rewrite the expression, and vice versa for f? What mathematical principle is behind this?

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# Why aren't these functions the same?

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