Bell RingerTECHNOLOGY

The surface area (in square millimeters) of a rectangular computer microchip is represented by the expression x2 - 12x + 35, where x is the number of circuits. If the width of the chip is (x - 5) millimeters, write a polynomial that represents the length.

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Pre-Requisite Skills Checklist

☑ 1. Can you add/subtract?

☑ 2. Can you multiply/simplify?

THEN YOU CAN DO THIS!!

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Are You Ready? The graph above shows the results of a survey that asked families how often they eat takeout. To determine what fractions of those surveyed eat takeout more than once a week, you can use addition. Remember that percents can be written as fractions with denominators of 100.

How is adding and subtracting rational expressions with like denominators similar to adding and subtracting rational numbers?

8%30%

22%

40%

How Many Times a Week Families Eat Takeout

Daily2-3 Times a weekonce a weekless often

What conditions must be met to add fractions?

Do you really need to change percents into fractions before adding them? Explain.

How do you simplify 38/100?

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Rational Expressions with Like DenominatorsSection 11-6

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Objectives

Add rational expressions with like denominators

Subtract rational expressions with like denominators

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Goals

Analyze various representations of rational functions with respect to problem situations.

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Key Concept

Add Rational Expressions

Recall that to add fractions with like denominators you add the numerators and then write the sum over the common denominator. You can add rational expressions with like denominators in the same way. Answers should always be expressed in simplest form.

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Example 1 p.608

a. Find 3n + 7n . 12 12

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Find each sum.

1A. 8x + 5x 6 6

1B. 4x + 7 5dy 5dy

Self-Check

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Example 2 p.609a. Find 2x + 2 . x + 1 x + 1

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Find each sum.

2A. 3y + y2 3 + y 3 + y

2B. 4x + 7 5dy 5dy

Self-Check

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Example 3 p.609GEOMETRY Find an expression for the perimeter of parallelogram PQRS. Remember that opposite sides of a parallelogram have the same length.

P = 2l + 2w

RS

QP

2 + 2( ) ( )

4a + 5b 3a + 7b

2a + 3b3a + 7b

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2a + 3b3a + 7b

4a + 5b 3a + 7b2 + 2( ) ( )

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Find an expression for the perimeter of each figure.

3A. 3B.

Self-Check

2t + 1 t + 2

2t + 1 t + 2

2t . t + 2

8h - 14 h + 1

7 . h + 1

5h + 1 h + 1

5h + 1 h + 1

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Example 4 p.610a. Find 3x + 4 - x - 1 x - 2 x - 2

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b. Find 3m - 5 - 4m + 2 m + 4 m + 4

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Find each difference.

4A. 2h + 4 - 5 + h h + 1 h + 1

4B. 17h + 4 - 2h - 6 15h - 5 15h - 5

Self-Check

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Example 5 p.610Find 2m + 4m m - 9 9 - m

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Find each sum.

5A. 3n + 6n n - 4 n - 4

5B. t2 + 3 t - 3 3 - t

Self-Check

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Homework

Practice 11-6 WSevens or odds

p. 613Spiral Review42 - 50 even

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