Properties of Algebraic Fractions (Rational Expressions)
Big Idea: An algebraic fraction (also called a rational expression) is a fraction where the numerator, denominator, or both contain variables. Just like numerical fractions, algebraic fractions follow specific properties that allow us to simplify, compare, and manipulate them.
Quick Review: From Numbers to Variables
You already know that $\frac{2}{3} \times \frac{5}{5} = \frac{10}{15}$ — the value doesn't change when we multiply by 1. The same principle applies to algebraic fractions:
$$\frac{x}{x+1} \times \frac{x-2}{x-2} = \frac{x(x-2)}{(x+1)(x-2)}$$
Now let's formalize all the key properties using algebraic expressions.