Add or subtract, as indicated. (7x + 8)/(3x + 2) - (x + 4)/(3x + 2)

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including addition and subtraction, is crucial for solving problems involving them. In this case, both expressions share a common denominator, which simplifies the process of combining them.

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions. When adding or subtracting rational expressions, it is essential to have a common denominator to combine the numerators correctly. In the given question, both fractions have the same denominator, which allows for straightforward subtraction of the numerators.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This concept is vital when simplifying the result after performing operations on rational expressions. In the context of the question, after finding a common denominator, the next step is to combine the resulting terms in the numerator.