Algebra Demystified 2nd Ed

54 algebra De mystif ieD

deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter2

6.

(^127)
623
12
7
23
6
12
7
6
23
72
161
x
y
x
y
=÷=⋅xy= xy^

7.^33
1

2

9

3

1

9

2

27

92 y y^2

=÷ =⋅ =yy^

8.

x 2 xxx

52

5

12

1

510

=÷=⋅=

Adding and Subtracting Fractions Containing Variables

When adding or subtracting fractions with variables, we treat the variables as if

they were prime numbers. If a variable appears in the denominator, the LCD

has the variable, too.

EXAMPLES

Find the sum.

6

25 4

6

25

4

44

25

25

24

100

25

100

24 25

100

+= ⋅+⋅=yy+=yy+

2

15

14

33

2

15

11

11

14

33

5

5

22

165

70

165

tt+=⋅+⋅= +=tt 22 + 70

1165

18 3

4

18 4

4

3

4

72

4

3

4

72 3

xx 4

x

xx

x

x

x

x

−= ⋅−⋅=−=−

9

16

5

t 12

+

16 t = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅t and 12 = 2 ⋅ 2 ⋅ 3 so the LCD = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ t = 48t

48 t ÷ 16 t = 3 and 48t ÷12 = 4t^48

16

3 48

12

t 4

t

 ==t t







and

9

16

5

t 12

+ =⋅+⋅=+^9 = +

16

3

3

5

12

4

4

27

48

20

48

27 20

t 48

t

tt

t

t

t

t

71

84

13

30

−

x

84 = 2 ⋅ 2 ⋅ 3 ⋅ 7 and 30x = 2 ⋅ 3 ⋅ 5 ⋅ x

EXAMPLES

Find the sum.