Section 6.2 Adding & Subtracting Rational Expressions

6.2 1

Section 6.2 Adding & Subtracting Rational Expressions

Adding & Subtracting Rational Expressions with the Same Denominators

Finding the LCD of 2 or more Polynomial Denominators Adjusting Opposite Factors in Denominators Adding & Subtracting Rational Expressions

with Unlike Denominators 1 1 ? ------------- + -------------- = ----------------

6.2 2

Adding and Subtracting Fractions with Identical Denominators

Perform the operation:

6.2 3

Finding the LCD (must be done before adding or subtracting 2 or more RE’s)

1. Factor each denominator completely into primes.

2. List all factors of each denominator. (use powers when duplicate factors exist)

3. The LCD is the product of each factor to its highest power.

28z3 = (22) (7)(z3) 321z = (3)(7) (z) 4z2

LCD= (22)(3)(7)(z3) Lacks↑

(a2 – 25) = (a + 5)(a – 5) (a + 2)(a + 7a + 10) = (a + 5) (a + 2) (a – 5) LCD = (a + 5)(a – 5)(a + 2) Lacks↑

33

2

2

4

4

z

z

)2()2(

aa

)5()5(

aa

6.2 4

? ? ? 8(x – 3) (x2 – x – 6) (2x2 – 12x + 18) 8(x – 3) = (2)3(x – 3) (x + 2)(x – 3) (x2 – x – 6) = (x – 3)(x + 2) 8(x – 3) (2x2 – 12x + 18) = (2) (x – 3)2 4(x + 2) LCD = (2)3 (x – 3)2(x + 2) Lacks↑

Find the LCD, using a Primes Table

6.2 5

Adjusting an Opposite Denominator Situation: one factor is the opposite of the other For 7 and 2 find the LCD

3(a – 2) (2 – a) For the second expression, multiply top and

bottom by -1 (doesn’t change its value) Now 7 and -2 find the LCD

3(a – 2) (a – 2) Do this after factoring, before writing the LCD

6.2 6

1. Find the LCD.2. Express each rational

expression with a denominator that is the LCD.

3. Add (or subtract) the resulting rational expressions.

4. Simplify the result if possible.

Adding or subtracting rational expressions with unlike denominators – note any exclusions

Exclusions: a ≠ ±2

6.2 7

Add & Subtract Practice - monomials

222 21352

7375

212

35

212

xx

xxxx

xx

LacksxLCD

xx

xxx

2

22

)7)(3(

7)3(3

)7)(3(21

Exclusions: x ≠ 0

6.2 8

Add & Subtract Practice - simplifying

2

2

22

2

2

2

2222

2

)(22

)()(2

)(

))(()(2

)(22

2

yxyxx

yxyx

yxx

yxyxyx

yxx

yxyx

yxyxx

LacksyxLCD

yxyxyxyxyxyx

2

222

)(

)()(1)(2

6.2 9

Add & Subtract Practice – change both

)1)(6)(1(4

)1)(6)(1(32132

)1)(6)(1()1)(3()1)(12(

653

6712

222

22

yyyyy

yyyyyyy

yyyyyyy

yyy

yyy

LacksyyyLCD

yyyyy

yyyyy

)1)(6)(1(

)1()1)(6(65

)1()6)(1(672

2

Exclusions: y ≠ ±1, 6

6.2 10

Brain Break:

6.2 11

Add & Subtract – opposite monomials

aaaaaa 41

82

81

83

81

83

aLCD 8

Exclusions: a ≠ 0

6.2 12

Add & Subtract – opposite binomials

yxyx

yxy

yxx

xyy

yxx

2735

2)73(1

25

273

25

xyLCD 2

+

6.2 13

Add & Subtract – function simplification

24

)2)(2()2(4

)2)(2(84

)2)(2(21052

)2)(2()2()2(52)(

21

25

)2)(2(2)(

21

25

42)( 2

xxxx

xxx

xxxxx

xxxxxxf

xxxxxxf

xxxxxf

)2)(2(

)2(2)2(2)2)(2(42

xxLCD

xxxxxxx

Exclusions: x ≠ ±2

6.2 14

What Next? 6.3 Complex Fractions

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