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

Verified step by step guidance

1. Identify the rational expression: $\frac{x^2-1}{x+1}$.
2. Recall that the domain of a rational expression is all real numbers except where the denominator is zero.
3. Set the denominator equal to zero to find the values that are not in the domain: $x+1=0$.
4. Solve the equation $x+1=0$ to find the value of $x$ that makes the denominator zero.
5. Exclude the value found in the previous step from the domain of the rational expression.

Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial because they can have restrictions on their values, particularly when the denominator is zero, which leads to undefined expressions.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational expressions, the domain excludes any values that make the denominator zero, as these would result in undefined expressions.

Finding Restrictions

To find the domain of a rational expression, one must identify the values that cause the denominator to equal zero. This involves solving the equation formed by the denominator and excluding these values from the domain, ensuring that the expression remains valid.