LESSON 8 1 Multiplying and Dividing Rational Expressions

LESSON 8– 1 Multiplying and Dividing Rational Expressions

Five-Minute Check (over Chapter 7) TEKS Then/Now New Vocabulary Example 1: Simplify a Rational Expression Example 2: Determine Undefined Values Example 3: Simplify Using – 1 Key Concept: Multiplying Rational Expressions Example 4: Multiply and Divide Rational Expressions Example 5: Polynomials in the Numerator and Denominator Example 6: Simplify Complex Fractions

Over Chapter 7 Evaluate log 12 7. A. 2. 4849 B. 1. 9459 C. 0. 7831 D. 0. 5389

Over Chapter 7 A. B. C. D.

Over Chapter 7 Solve log 3 (x 2 – 12) = log 3 4 x. A. 6 B. 7 C. 8 D. 9

Over Chapter 7 Solve 5 ex – 3 = 0. A. – 0. 5108 B. – 0. 2197 C. 0. 2197 D. 0. 4979

Over Chapter 7 Suppose $200 was deposited in a bank account and it is now worth $1100. If the annual interest rate was 5% compounded continuously, how long ago was the account started? Use the formula A = Pert. A. about 42 years ago B. about 34 years ago C. exactly 29 years ago D. about 24 years ago

Over Chapter 7 Suppose the population of New York State grows at a rate of 0. 3% compounded continuously. In 2006, the population was 19. 3 million. Write an equation that represents the population and predict the population in after t years 2020. A. y = 19. 3 e(0. 003)t; about 20. 1 million B. y = 19. 3 e(0. 03)t; about 29. 4 million C. y = 19. 3 e(1. 003)t; about 52. 6 million D. y = 19. 3 e(1. 3)t; about 70. 8 million

Targeted TEKS A 2. 7(F) Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two. Mathematical Processes A 2. 1(E), A 2. 1(F)

You factored polynomials. • Simplify rational expressions. • Simplify complex fractions.

• rational expression • complex fraction

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

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.

A. Simplify A. B. C. D. .

B. Under what conditions is the expression undefined? A. x = 4 or x = – 4 B. x = – 5 or x = 4 C. x = – 5, x = 4, or x = – 4 D. x = – 5

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

Determine Undefined Values Solve the 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. p 2 – 2 p – 15 = (p – 5)(p + 3) Factor the denominator. p – 5 = 0 or p + 3 = 0 Zero Product Property p =5 Answer: B p = – 3 Solve each equation.

For what value(s) of p is A. – 5, – 3, – 2 B. – 5 C. 5 D. – 5, – 3 undefined?

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

Simplify A. y – x B. y C. x D. –x .

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

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

Multiply and Divide Rational Expressions Simplify. Answer:

A. Simplify A. B. C. D. .

B. Simplify A. Ans. A B. Ans. B C. Ans. C D. Ans. D .

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

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

Polynomials in the Numerator and Denominator Simplify. Answer:

A. Simplify A. B. C. 1 D. – 1 .

A. B. C. D.

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

Simplify Complex Fractions – 1 Factor. Simplify. Answer:

Simplify . A. e B. C. e D.

LESSON 8– 1 Multiplying and Dividing Rational Expressions