Find the domain of each rational expression. (2x - 4) / (x + 7)

Verified step by step guidance

1. Identify the rational expression: $\frac{2x-4}{x+7}$.
2. Understand 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: $x+7=0$.
4. Solve the equation $x+7=0$ to find the value of $x$ that makes the denominator zero.
5. The domain of the expression is all real numbers except the value of $x$ found in the previous step.

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 exhibit unique behaviors, particularly regarding their domains, which are influenced by the values that make the denominator zero.

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 cause the denominator to equal zero, as division by zero is undefined.

Finding Restrictions

To find the domain of a rational expression, one must identify the values of x that make the denominator zero. This involves setting the denominator equal to zero and solving for x, which reveals the restrictions that must be excluded from the domain.