Perform the indicated operation, and write each answer in lowest terms. 4/x-y - 9/x-y

Verified step by step guidance

1. Identify the common denominator for the fractions, which is \(x - y\).
2. Since both fractions already have the same denominator \(x - y\), you can combine them into a single fraction.
3. Subtract the numerators: \(4 - 9\).
4. Write the result as a single fraction: \(\frac{4 - 9}{x - y}\).
5. Simplify the numerator: \(4 - 9 = -5\), so the expression becomes \(\frac{-5}{x - y}\).

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including addition, subtraction, multiplication, and division, is crucial for solving problems involving them. In this case, the expressions involve a common denominator, which is essential for performing the indicated operation.

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions. When performing operations like addition or subtraction on rational expressions, it is necessary to express them with a common denominator to combine them correctly. In the given question, recognizing that both terms share the same denominator 'x - y' simplifies the operation.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing the numerator and denominator by their greatest common factor (GCF). This process is important for presenting answers in a clear and concise manner. After performing the operation in the question, simplifying the resulting expression ensures that the final answer is in its simplest form.