Write each rational expression in lowest terms. m^2 - 4m + 4 / m^2 + m - 6

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 the polynomials to identify common factors.

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process is crucial for simplifying rational expressions, as it allows us to cancel out common factors in the numerator and denominator. Techniques for factoring include finding the greatest common factor, using the difference of squares, and applying the quadratic formula for quadratic expressions.

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 completely and then cancel any common factors. This ensures that the expression is simplified to its most basic form, making it easier to work with in further calculations.