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I'm a student studying math, and I'm going through some old exam problems and I have come across a set of questions that ask me to decide where a given function is continuous . At first glance it appears the example above is continuous everywhere as $x = -1,1$. Is it as simple enough just to say, or am I missing something, like a rigours theorem of some sort?

Any help would be much appreciated.

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    $\begingroup$ Your first glance should be correct. $\endgroup$ – Mathsisfun May 22 '20 at 3:57
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The sum and product of continuous function is a continuous function, so it's enough to say that it will be continuous except for $x=-1, x=1$ since the function is undefined at those points

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  • $\begingroup$ So you say $\frac{x +3}{x^2-1}$ is continuous because ${x +3}$ and $\frac{1}{x^2-1}$ are continuous. Then the next question is, why is $\frac{1}{x^2-1}$ continuous? $\endgroup$ – miracle173 May 22 '20 at 5:27
  • $\begingroup$ $f(x)=x^2-1$ & $g(x)=1$ is continuous, so $g/f$ is continuous where $f \ne 0$. $\endgroup$ – Tamas Kanti Garai May 22 '20 at 6:14

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