Find the domain of each rational expression. x 2 - 1 / x + 1

Hello everyone. We're going to solve for the domain of the rational expression X squared minus 1 over X plus 12. I'm rewriting it so I can see my numerator by denominator clearly and I can work with it. So recall that the domain is all the X. Values that make our expression a true statement. We don't want any undefined values. Undefined values happen when the denominator equal zero. To find out when the denominator equal zero. We need to set the denominator equal to zero. So in this case X plus 12 would have to equal zero for us to find out where this happens. So solving I get that x equals negative 12. This means that our domain is all real numbers Except when x equals negative 12. Our answers however are an interval notation. So we need to write this out a little differently. We're going to write it out that our domain is from negative infinity to negative 12. Doesn't include the negative 12 And then goes from - to positive infinity. So this is my solution. And that would be answer choice a Have a good day

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Problem 17a

Textbook Question

Find the domain of each rational expression. x² - 1 / x + 1

Verified step by step guidance

Identify the rational expression given: \(\frac{x^2 - 1}{x + 1}\).

Recall that the domain of a rational expression includes all real numbers except those that make the denominator zero.

Set the denominator equal to zero to find the values to exclude: \(x + 1 = 0\).

Solve for \(x\): \(x = -1\).

Conclude that the domain is all real numbers except \(x = -1\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials. Understanding rational expressions involves knowing how to simplify, manipulate, and analyze these fractions, especially focusing on restrictions caused by the denominator.

Domain of a Function

The domain of a function is the set of all input values (x-values) for which the function is defined. For rational expressions, the domain excludes values that make the denominator zero, as division by zero is undefined.

Finding Restrictions by Setting the Denominator Equal to Zero

To find the domain of a rational expression, set the denominator equal to zero and solve for x. The solutions are excluded from the domain because they cause division by zero, which is undefined in mathematics.

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