Unit 3 Lesson 2: Rational Expressions

Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b , such that You can tell that a number is rational because its decimal is either _________________________ or ________________________. The rational numbers are closed under the four main operations (addition, subtraction, multiplication, and quotient division), which means that the sum, difference, product, and quotient of rational numbers are always ________________________. repeating terminating rational

Definition of a Rational Expression A rational expression has the form 𝑟 𝑥 = 𝑓(𝑥) 𝑔(𝑥) Where f(x) and g(x) are polynomials (g(𝑥)≠0)

Rewriting in Lowest Terms Example 1: State any restrictions on the variable.

Rewriting in Lowest Terms Example 2: State any restrictions on the variable.

Arithmetic Operations Example 3: State any restrictions on the variable.

Arithmetic Operations Example 4: State any restrictions on the variable.

Arithmetic Operations Example 5: State any restrictions on the variable.