CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x

Verified step by step guidance

1. Identify the common denominator for the fractions $\frac{3}{x}$ and $\frac{7}{x}$. In this case, the common denominator is $x$.
2. Since the denominators are already the same, you can add the numerators directly: $3+7$.
3. Combine the numerators over the common denominator: $\frac{3+7}{x}$.
4. Simplify the expression by adding the numerators: $\frac{10}{x}$.
5. Ensure the fraction is in its lowest terms. Since 10 and $x$ have no common factors other than 1, $\frac{10}{x}$ is already in its simplest form.

Key Concepts

Fractions

Fractions represent a part of a whole and are expressed as a ratio of two integers, where the numerator is the top number and the denominator is the bottom number. To perform operations with fractions, such as addition, it is essential to have a common denominator. In this case, the fractions 3/x and 7/x can be combined since they share the same denominator.

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions, allowing for their addition or subtraction. In the given problem, both fractions have the same denominator of 'x', which simplifies the addition process. When fractions have the same denominator, you can simply add the numerators while keeping the denominator unchanged.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To express a fraction in lowest terms, you can simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD). In this problem, after performing the addition, it is important to check if the resulting fraction can be simplified further.