1. Equivalent Rational Expressions Example 1: When we multiply both the numerator and the denominator of a rational number by the same non-zero value, we create an equivalent rational number.

2. Equivalent Rational Numbers Note that when we multiply both numerator and denominator by 5, we are actually multiplying the fraction by 1. The result is that the value of the fraction is not changed.

3. When we multiply both the numerator and the denominator of a rational expression by the same non-zero expression, we create an equivalent rational expression. Example 2: Equivalent Rational Expressions

4. Our goal is often to create an equivalent rational expression with a given denominator. Write the first rational expression as an equivalent rational expression with the given denominator. Example 3:

5. Determine what you would multiply times the denominator on the left to get the denominator on the right. The required factor is

6. Multiply both numerator and denominator by the expression … … to get the equivalent rational expression with the required denominator.

7. Example 4: Factor the denominator of the rational expression on the left. Write the first rational expression as an equivalent rational expression with the given denominator.

8. We need Determine what you would multiply times the denominator on the left to get the denominator on the right.

9. We need Determine what you would multiply times the denominator on the left to get the denominator on the right.

10. Multiply both numerator and denominator by the expression … … to get the equivalent rational expression with the required denominator.