Question B.5.1: Domain of a rational expression Find the domain of each rati...
Domain of a rational expression
Find the domain of each rational expression.
a. \frac{2 x-1}{x+3} b. \frac{2 x+4}{(x+2)(x+3)} c. \frac{1}{x^{2}+8}
a. The domain is the set of all real numbers except those that cause x + 3 to have a value of 0. So -3 is excluded from the domain, because x + 3 has a value of 0 for x = -3. We write the domain in set notation as \{x \mid x \neq-3\}.
b. The domain is the set of all real numbers except -2 and -3, because replacing x by either of these numbers would cause the denominator to be 0. The domain is written in set notation as \{x \mid x \neq-2 and x \neq-3\}.
c. The value of x^{2}+8 is positive for any real number x. So the domain is the set of all real numbers, R.
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