In Exercises 33–68, add or subtract as indicated. 5/x + 3

Verified step by step guidance

1. Identify the terms in the expression: $\frac{5}{x}+3$.
2. Recognize that $\frac{5}{x}$ is a rational expression and 3 is a constant.
3. To add or subtract rational expressions, they must have a common denominator. Here, the denominator is $x$.
4. Rewrite the constant 3 as a fraction with the same denominator: $\frac{3x}{x}$.
5. Combine the fractions: $\frac{5}{x}+\frac{3x}{x}=\frac{5+3x}{x}$.

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions is crucial for performing operations like addition and subtraction. In the given question, '5/x' is a rational expression, and recognizing its structure helps in combining it with other terms.

Common Denominator

To add or subtract rational expressions, it is essential to find a common denominator. This involves identifying a denominator that can accommodate all terms involved in the operation. In the example '5/x + 3', the number '3' can be expressed as '3x/x' to create a common denominator of 'x', allowing for the addition of the two terms.

Simplifying Expressions

After performing operations on rational expressions, simplifying the result is important for clarity and ease of understanding. This involves combining like terms and reducing fractions to their simplest form. In the context of the question, after finding a common denominator and adding the terms, simplifying the resulting expression will yield the final answer.