Algebra Demystified 2nd Ed

Chapter 2 IntroduCtIon to VarIables 49

deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter 2

3.^30
16

15

8

2

2

15

8

xy

y

xy

y

=⋅= x

4.^72
18

418

18

x 4

xy y

x

xy

=⋅ =^

5. xx
   x

xx

x

()− (^6) = − ⋅=x−
2
6
2
6
2

6.^621
3

22 1

1

3

3

xy x 22 1

x

yx x

x

()()− = − ⋅=yx()−

7. ()()
   ()

5162 7

62 7

516

6

27

27

516

6

xx

x

xx

x

++ x

+

= + ⋅ +

+

= +

8.^2481
15 8

81

5

38

38

xy x 8

xy

xxy

xy

()()

()

()()

()

++ (

+

= + ⋅ +

+

= xx+^1

5

)

9.^15021783
48

25 2178 3

8

6

6

25

xy xx

y

xx xy

y

()+−()= ()+−()⋅

= xxx()^2178 ()x^3

8

+−

Operations on Fractions Containing Variables

Multiplication of fractions with variables is done in exactly the same way as

multiplication of fractions without variables—we multiply the numerators and

multiply the denominators and divide out common factors.

EXAMPLES

Find the product.

7

10

3

4

73

10 4

21

40

⋅=⋅

⋅

xx= x

24

5

3

14

24 3

514

12 3

57

36

y yyy 35

⋅=⋅

⋅

= ⋅

⋅

=

34

15

3

16

34 3

15 16

17 1

58

17

40

xx⋅= ⋅ xx

⋅

= ⋅

⋅

=

EXAMPLES

Find the product.