6.6 Simplifying Rational Expressions

The of two polynomials is called a expression. A function that is defined by a quotient of two polynomials and is written in simplest form is called a . In no case can the be To reduce a fraction into lowest terms, we can common factors in both the numerator and denominator. quotient rational rational function denominator zero cancel

Example: Simplify. First, factor both the numerator and denominator. Then, determine which values x cannot be (what makes the denominator zero) Finally, cancel any common factors and rewrite the expression.

Simplify. 1.

Simplify. 2.

Simplify. 3.

Simplify. 4.