Math CentralQuandaries & Queries


Question from Minks:

Find the domain of the function

(x^2 + 1 / x^2 +2x - 3 ) X ( x^2 -9 / x^2 - 2x - 3)

Hi Minks,

It is often easier to find the values of $x$ that are not in the domain of the function, that is the values of $x$ for which the function doesn't yield a legitimate value. Look at your function

\[\frac{x^2 + 1}{x^2 +2x - 3} \times \frac{x^2 -9}{x^2 - 2x - 3}.\]

If you substitute a value of $x$ into this expression you get a real number except if one on the denominators is zero. Factor both denominators, find the values of $x$ that make the denominators zero and then the domain of the function is all real numbers $x$ except the ones that make a denominator equal to zero.

I hope this helps,

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