Look for common factors. Simplify a Rational Expression A. Simplify . Look for common factors. Eliminate common factors. ● Simplify. Answer: Example 1A

B. Under what conditions is the expression undefined? Simplify a Rational Expression B. Under what conditions is the expression undefined? Just as with a fraction, a rational expression is undefined if the denominator equals zero. The original factored denominator is (y + 7)(y – 3)(y + 3). Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3. Example 1B

For what value(s) of p is undefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3 Undefined Values For what value(s) of p is undefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3 Read the Test Item You want to determine which values of p make the denominator equal to 0. Example 2

p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator. Undefined Values Solve the Test Item Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator. p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator. p – 5 = 0 or p + 3 = 0 Zero Product Property p = 5 p = –3 Solve each equation. Answer: B Example 2

Factor the numerator and the denominator. Simplify Using –1 Simplify . Factor the numerator and the denominator. b – 2 = –(–b + 2) or –1(2 – b) Simplify. Answer: –a Example 3

Concept

A. Simplify . Simplify. Simplify. Answer: Multiply and Divide Rational Expressions A. Simplify . Simplify. Simplify. Answer: Example 4A

Multiply by the reciprocal of the divisor. Multiply and Divide Rational Expressions B. Simplify Multiply by the reciprocal of the divisor. Simplify. Example 4B

Multiply and Divide Rational Expressions Simplify. Answer: Example 4B

A. Simplify . Factor. 1 + k = k + 1, 1 – k = –1(k – 1) = –1 Simplify. Polynomials in the Numerator and Denominator A. Simplify . Factor. 1 + k = k + 1, 1 – k = –1(k – 1) = –1 Simplify. Answer: –1 Example 5A

Multiply by the reciprocal of the divisor. Polynomials in the Numerator and Denominator B. Simplify . Multiply by the reciprocal of the divisor. Factor. Example 5B

Simplify. Answer: Polynomials in the Numerator and Denominator Example 5B

Express as a division expression. Simplify Complex Fractions Simplify . Express as a division expression. Multiply by the reciprocal of the divisor. Example 6

Simplify Complex Fractions Factor. –1 Simplify. Answer: Example 6