section 9.4 combining operations and simplifying complex rational expressions

Section 9.4 Combining Operations and Simplifying Complex

Rational Expressions

9.4 Lecture Guide: Combining Operations and Simplifying Complex Rational Expressions

Objective 1: Simplify rational expressions in which the order of operations must be determined.

Order of Operations

Step 1. Start with the expression within the _____________________ pair of grouping symbols.

Step 2. Perform all exponentiations.

Step 3. Perform all _____________________ and divisions as they appear from left to right.

Step 4. Perform all additions and _____________________ as they appear from left to right.

Use the correct order of operations to simplify each expression.

1.3

2

8 4 5

3 12

x x

x

Use the correct order of operations to simplify each expression.

2.3

2

8 4 5

3 12

x x

x

Use the correct order of operations to simplify each expression.

3. 3 1 3 1

4 4x x

Use the correct order of operations to simplify each expression.

4.23

2

1 3

3

x

x x x

Objective 2: Simplify complex fractions.

A complex rational expression is a rational expression where the numerator and/or the denominator also contain _______________. It is very important to identify the "main fraction bar" in a complex fraction

Simplify:

5.

125

Simplify:

6.125

Simplify by rewriting each expression with the division symbol ÷. Assume the variables are restricted to values that prevent division by zero.

7.2 9

2 64

xxx

8.

2 2

2

2 2

3

235

49

x xy yx

x yx

Simplify by rewriting each expression with the division symbol ÷. Assume the variables are restricted to values that prevent division by zero.

9.2

3 5

53

x xx

Simplify by rewriting each expression with the division symbol ÷. Assume the variables are restricted to values that prevent division by zero.

10.2

3 246

2 12 3

xx x

x x

Simplify by rewriting each expression with the division symbol ÷. Assume the variables are restricted to values that prevent division by zero.

Simplify by multiplying both the numerator and the denominator by the LCD of all terms. Assume the variables are restricted to values that prevent division by zero.

11.

13

35 16 4

12.2

2

6 51

251

x x

x

Simplify by multiplying both the numerator and the denominator by the LCD of all terms. Assume the variables are restricted to values that prevent division by zero.

Simplifying expressions containing negative exponents (Two Methods):

13. Simplify by converting each term with

negative exponents to an expression with positive exponents. Assume that x is restricted to values that prevent division by zero.

1 2

1 2

1 2x x

x x

Simplifying expressions containing negative exponents (Two Methods):

14. Simplify by multiplying the numerator

and the denominator by the lowest power of x that will eliminate all of the negative exponents on x. Assume that x is restricted to values that prevent division by zero.

1 2

1 2

1 2x x

x x

15. Simplify and assume the variables are restricted to values that prevent division by zero.

1 2 3

1

9 20

1 5

x x x

x

6x cm

10x cm

x cm

16. Write an expression that represents the area of this trapezoid.