Write each rational expression in lowest terms. 8k + 16 / 9k + 18

Verified step by step guidance

1. Identify the numerator and denominator of the rational expression: numerator is \$8k + 16\( and denominator is \)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 rational expression using the factored forms: \(\frac{8(k + 2)}{9(k + 2)}\).
5. Cancel the common factor \((k + 2)\) from numerator and denominator, assuming \(k \neq -2\), to simplify the expression to \(\frac{8}{9}\).

Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials. Simplifying rational expressions involves factoring and reducing common factors, similar to simplifying numerical fractions.

Factoring Polynomials

Factoring involves rewriting a polynomial as a product of its factors. Common techniques include factoring out the greatest common factor (GCF), which is essential for simplifying expressions by canceling common terms.

Simplifying Rational Expressions

To simplify a rational expression, factor both numerator and denominator completely, then cancel any common factors. This process reduces the expression to its lowest terms, making it easier to work with or interpret.