Find the domain of each rational expression. See Example 1.

x² ...

Question

Find the domain of each rational expression. See Example 1.

x² - 1
————
 x + 1

Accepted Answer

Hello, everyone. We are asked for the following rational expression to find its domain. The expression we are given is in parentheses, M squared minus nine divided by the parentheses. M plus three. Our answer choices are a, the interval from negative infinity to negative three without negative three included union with the interval from negative three to positive infinity. Without negative three included B the interval from negative infinity to three union with the interval from three to positive infinity. Not including the end points of three C, the interval from negative infinity to negative three union with the interval from negative 3 to 3 union with the interval three to positive infinity without negative three or three. As end points included D the interval from negative infinity to positive infinity. Rewriting this expression I again have M squared minus nine and I'm gonna write it as a fraction. So it's gonna be divided by M plus three is my denominator. So I recall that a domain is all the X values A function covers or a expression covers. And that I need to find where is this undefined? And I recall that it is undefined when the denominator equals zero. So we're gonna find out what M value would make our denominator zero to do that. We're gonna do M plus three equals zero. Solving for M we get that this is undefined when M equals negative three. So this is a hole in our domain. So all the other real numbers should be covered. So we could go from negative infinity till we get to negative three. And then we don't include the negative three. So that's a parentheses. But we're gonna union that with the interval that goes from negative three to positive infinity because the only hole in our domain is at negative three. So this is our answer the interval from negative infinity to three, negative three union with the interval from negative three to positive infinity without the negative three included. And that's answer choice. A have a nice day.

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Find the domain of each rational expression. See Example 1. x² - 1 ———— x + 1