SWBAT…simplify rational expressions Wed, 4/3Agenda

1. WU (15 min)2. Lesson on rational expressions (25 min)

-6 examples

1.) Factor 7x – 72.) Factor 8x – 83.) Factor x2 – 14.) Factor x2 – 95.) Factor x2 – 3x – 106.) x3 + 3x2

HW#3: Dividing Monomials

Simplifying Rational Expressions

Multiplying &Dividing Rational Expressions

Remember that a rational number can be expressed as a quotient of two integers.

A rational expression can be expressed as a quotient of two polynomials.

3

1

2

13

2

Remember, denominators can not = 0.

Examples of rational expressions

2

4 8 4 7, ,

3 3 5 9

x y

x x y y

For what values of x is each rational expression undefined?

1

9 and ,

3

2 ,

1 2

x

x

xx

x = 0 x = -3 x = 1

Simplify: 7x 7

x2 1

Step 1: Factor the numerator and the denominator completely looking for common factors.

7x 7 7(x 1)

x2 1 (x 1)(x 1)

Next

Ex. 1

7x 7

x2 1

7(x 1)

(x 1)(x 1)

What is the common factor?

x 1Step 2: Divide the numerator and denominator by the common factor.

7(x 1)

(x 1)(x 1)

7(x 1)

(x 1)(x 1)

1

1

Step 3: Multiply to get your answer.

Answer: 7

x 1

Looking at the answer from the previous example, what value of x would make the denominator 0?

x = -1

The expression is undefined when the values make the denominator equal to 0

1

882

x

x)1)(1(

)1(8

xx

x 1

11

8

x

54

1032

2

xx

xx

)5)(1(

)5)(2(

xx

xx

)1(

)2(

x

x1

1

Ex. 2

Ex. 3

9

652

2

x

xx

)3)(3(

)3)(2(

xx

xx

)3(

)2(

x

x1

1

Ex. 4

Remember how to multiply fractions:

First you multiply the numerators then multiply the denominators.

5 2:

6 20Ex 10 1

120 12

5 2

6 20

Ex: x3 3x2

x2 5x 6

x2 10x 9

x2 6x 27

Step #1: Factor the numerator and the denominator.

x2 (x 3)

(x 6)(x 1)

(x 1)(x 9)

(x 9)(x 3)

Next

Ex. 5

Step #2: Divide the numerator and denominator by the common factors.

x2 (x 3)

(x 6)(x 1)(x 1)(x 9)

(x 9)(x 3)1

1

1

1

1

1

Step #3: Multiply the numerator and the denominator.

x2

x 6

Multiply by the reciprocal of the divisor.

4

5

16

25

4

5

25

16

4 25

516

1

1

5

4

5

4

Remember how to divide fractions?

Dividing rational expressions uses the same procedure.

Ex. 6: Simplify

y 2

y2 10 y 24

y2 2y

y2 2y 8

y 2

y2 10 y 24

y2 2y

y2 2y 8

y 2

y2 10 y 24

y2 2y 8

y2 2y

y 2

(y 12)(y 2)(y 4)(y 2)

y(y 2)

1 1

1 1

4

( 12)

y

y y

Do HW#6 Problems 1 – 10

FYI: All problems were taken from college math placement tests

Additional Examples:

x 3

x2 4x 12

2x2 6x

x 2

Ex. 7

Ex. 8

Ex. 9

1) x + 3

2x3 2x2

x2 7x 6

x2 10x 21

2) 3x 67x 7

5x 1014x 14

Answers:

1) x 6

2x2 (x 7)

2) 6(x 1)5(x 1)

Answer: 1

2x(x 6)