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

Question

Find the domain of each rational expression. See Example 1. (x³ - 1) / (x - 1)

Accepted Answer

Hello, everyone. We are asked for the following rational expression to determine its domain. The expression we are given is the parentheses J cubed minus 27 divided by the parentheses J minus three. Our answer choices are a, the interval from negative infinity to three union with the interval from three to positive infinity. Neither end point at three is included B the interval from negative infinity to negative three, which negative three is not included union with the interval from negative three to positive infinity. Not including negative three C, the interval from negative infinity to negative three, not including negative three union with the interval from negative 3 to 3, not including either end points union with the interval from three to positive infinity. Not including three or D, the interval from negative infinity to positive infinity to begin, I'm gonna rewrite my expression as a fraction. So I have J cubed minus 27 divided by J minus three. And I recall that a domain is all the X values that this covers and that it should be all real numbers unless there's a spot where this is undefined. So if our expression is undefined, that means that the denominator equals zero and that would be a hole in our domain. So to find out what that could be, we're gonna set our denominator equal to zero. So J minus three will equal zero, adding three to both sides. We find that this expression is undefined when J equals three. So this means our domain is all real numbers except the value three. So what that looks like an interval notation is open parentheses, negative infinity to three, close parentheses because the three is not included union with open parentheses, three to positive infinity. Because again, the three is not included and that will be our domain and that matches answer choice a have a nice day.

Find the domain of each rational expression. See Example 1. (x³ - 1) / (x - 1)

Key Concepts

Domain of a Rational Expression

Factoring Polynomials

Difference of Cubes Formula

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