R5 - 1

Class Problems (10/07/15): Sec. R.5 Due in 15 minutes. (Write the problem and solve.) wire basketDetermine the domain.

1. 2.

Write in lowest terms.

3. 4.

Find each product or quotient.

5. 6.

2 4 2128

x x 2

2

4 37 10

k kk k

20 1030 15rr

8 42 4

yy y

23 15 10 254 20 12 60m m mm m

2 52 89 27r r

I will start Part II at

12:30 PM.

R5 - 2

Assignment – Sec. R.5: p. 47 (1-6 all, 11-33 odd) Due on Friday, 09 October 2015.Find the domain of each rational expression.

1 ) 36

xx

4) 2 27

xx

3 7 4 2 1

3) xx x

23 6) 5 6x x2

12 5

5)6x x

9 12 4)

2 3 5x

x x

Write each rational expression in lowest terms.

8 16 9

1518

) kk

3 313)

5 3t

t t

2

211 8 16) 4x xx

2

24 4 )

617 m m

m m

2

28 61 9

16 99) m m

m

3 64 2 ) 14

xx

R5 - 3

Assignment – Sec. R.5: p. 47 (1-6 all, 11-33 odd) Due on Friday, 09 October 2015.Find each product or quotient.

3

2 215 6 9 0

21

3) p pp p

2 8 3 12 2 )2

56k k

2

24 12 9 2 1

)0

220

9 a aa a a

22 5 )

57 2x x

xy y

2 2

2 23 2 5 6 5 4

3 )24

310

m m m mm m m m

2 2

2 212 9 20

2 1)

531

8 16p p p pp p p p

R-4

Rational ExpressionsR.5Addition and Subtraction ■ Complex Fractions

• Sec. R.5: p. 48 (41-55 odd, 59-75 odd)– WRITE THE PROBLEM and follow directions– Due Tuesday, 13 October 2015.

R-5

Adding and Subtracting Rational Expressions

Add

Find the LCD:

4 2 2

2 2

10 2 5

15 3 5

z z zz z

2 25 2 3z z 430z

R-6

Adding and Subtracting Rational Expressions

Add

R-7

Adding and Subtracting Rational Expressions

Subtract

Find the LCD:

R-8

Simplifying Complex Fractions

Simplify

Multiply the numerator and denominator by the LCD of all the fractions, k.

56

51

k

k

55 66

5 51 1

k

kk

kk

k

6 55

kk

R-9

Simplifying Complex Fractions

Simplify

Multiply the numerator and denominator by the LCD of all the fractions, x2.

2

2

3 46 1xx

R-10

Simplifying Complex Fractions

Simplify

Multiply the numerator and denominator by the LCD of all the fractions, a(a + 1).

11

1 11

aa a

a a

11

1

111

1 1 1 11 1

aaa a

a a

a a

a a

a a a a

11 1 1

1a aa aa

2 1

1a aa a

2 12 1a aa

R-11

Simplifying Complex Fractions

Simplify

Multiply the numerator and denominator by the LCD of all the fractions, z(z + 1)(z – 1).

1 11 1 1

1 11 1

z z z zz z z z

R-12

Assignment

• Sec. R.5: p. 48 (41-55 odd, 59-75 odd)– WRITE THE PROBLEM and follow directions– Due Tuesday, 13 October 2015.

Assignment: Sec. R.5: p. 48 (41-55 odd, 59-75 odd)Due Tuesday, 13 October 2015.Write the problem. Then perform each addition or subtraction.

R-13

3 5 2

43

1)k k

1 2 4 6

43)5

mm m m

21 45) ba a

1 1 51)x z x z

17 3 10 18 9 7

49)9 7

y yy y

25 11

61247)

xyx y

3 1

253)

2a a

2 2

55)2

x y xx y y x

2 25 3

12)

69

1x x

x x x

Assignment: Sec. R.5: p. 48 (41-55 odd, 59-75 odd)Due Tuesday, 13 October 2015.

R-14

Write the problem. Then simplify each expression.

11

161

1) x

x

21

69) 4 1

2

mm

m

1 1

163 1) x x

x

1 1

75) x h xh

11165) 111

b

b

3 41 7 )

1

3 1

yy yyy y

23

171 ) 6 1

4

pp

p

3 3

2 2

1

67) 1

2

a b

a ab b