10-1 Inverse Variation

10-2 Rational Functions

10-3 Simplifying Rational Expressions

10-4 Multiplying and Dividing Rational Expressions

10-5 Adding and Subtracting Rational Expressions

10-6 Dividing Polynomials

10-7 Solving Rational Equations

10-8 Applying Rational Equations

PreviewPreview

Warm Ups

Warm UpSolve each proportion.

1.

2.

3. 4.

5. The value of y varies directly with x, and y = –6 when x = 3. Find y when x = –4.

6. The value of y varies directly with x, and y = 6 when x = 30. Find y when x = 45.

10 4.2

2.625 2.5

8

9

10-1 Inverse Variation

Warm Up

The inverse variation xy = 8 relates the constant speed x in mi/h to the time y in hours that it takes to travel 8 miles. Graph this inverse variation.

10-2 Rational Functions

Warm Up

Simplify each expression.

1. 2.

Factor each expression.

3. x2 + 5x + 6 4. 4x2 – 64 (x + 2)(x + 3) 5. 2x2 + 3x + 1 6. 9x2 + 60x + 100 (2x + 1)(x + 1)

4(x + 4)(x – 4)

(3x +10)2

10-3 Simplifying Rational Expressions

Warm UpMultiply.

1. 2x2(x + 3) 2. (x – 5)(3x + 7)

3. 3x(x2 + 2x + 2) 4. Simplify .

Divide. Simplify your answer.

5. 6. 7. 8.

2x3 + 6x23x2 – 8x – 35

3x3 + 6x2 + 6x

10-4 Multiplying and Dividing Rational Expressions

Warm Up

Add. Simplify your answer.

1. 2.

3. 4.

Subtract. Simplify your answer.

5.

7.

6.

8.

10-5 Adding and Subtracting Rational Expressions

Warm Up

Divide.

1. m2n ÷ mn4 2. 2x3y2 ÷ 6xy

3. (3a + 6a2) ÷ 3a2b

Factor each expression.

4. 5x2 + 16x + 12

5. 16p2 – 72p + 81

10-6 Dividing Polynomials

Warm Up

1. Find the LCM of x, 2x2, and 6.

2. Find the LCM of p2 – 4p and p2 – 16.

Multiply. Simplify your answer.

3. 4.

5.

10-7 Solving Rational Equations

Warm UpMultiply. Simplify your answer.

1.

3.

Solve

2.

4.

5.

1

10-8 Applying Rational Equations