Write each rational expression in lowest terms. 3(3 - t) / (t + 5)(t - 3)

Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. To work with rational expressions, it is essential to understand how to manipulate polynomials, including addition, subtraction, multiplication, and division. Simplifying these expressions often involves factoring polynomials to identify common factors.

Factoring Polynomials

Factoring polynomials is the process of breaking down a polynomial into simpler components, or factors, that when multiplied together yield the original polynomial. This is crucial for simplifying rational expressions, as it allows for the cancellation of common factors in the numerator and denominator. Techniques include finding the greatest common factor (GCF) and using special products like the difference of squares.

Lowest Terms

A rational expression is said to be in lowest terms when the numerator and denominator have no common factors other than 1. To express a rational expression in lowest terms, one must factor both the numerator and denominator and cancel any common factors. This process ensures that the expression is simplified as much as possible, making it easier to work with in further calculations.