Write each rational expression in lowest terms. See Example 2. (8k + 16) / (9k + 18)

Verified step by step guidance

1. Identify the rational expression given as a fraction: \(\frac{8k + 16}{9k + 18}\).
2. Factor out the greatest common factor (GCF) from the numerator: \$8k + 16 = 8(k + 2)$.
3. Factor out the greatest common factor (GCF) from the denominator: \$9k + 18 = 9(k + 2)$.
4. Rewrite the expression using the factored forms: \(\frac{8(k + 2)}{9(k + 2)}\).
5. Cancel the common factor \((k + 2)\) from numerator and denominator to simplify the expression to \(\frac{8}{9}\), assuming \(k \neq -2\) to avoid division by zero.

Key Concepts

Factoring Polynomials

Factoring involves rewriting a polynomial as a product of its factors. For expressions like 8k + 16, factoring out the greatest common factor (GCF) simplifies the expression, making it easier to reduce rational expressions.

Simplifying Rational Expressions

A rational expression is simplified by dividing the numerator and denominator by their common factors. This process reduces the expression to its lowest terms, ensuring no further simplification is possible.

Greatest Common Factor (GCF)

The GCF is the largest factor shared by two or more terms. Identifying the GCF in both numerator and denominator is essential to factor and simplify rational expressions effectively.