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

Verified step by step guidance

1. Identify the rational expression given: \(\frac{x^2 - 1}{x + 1}\).
2. Recall that the domain of a rational expression includes all real numbers except those that make the denominator zero.
3. Set the denominator equal to zero to find the values to exclude: \(x + 1 = 0\).
4. Solve for \(x\): \(x = -1\).
5. Conclude that the domain is all real numbers except \(x = -1\).

Key Concepts

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.