Algebra Demystified 2nd Ed

378 alGEbra De mystif ieD

4.^21
1

3

2

87

2

2

2

x

x

x

x

x

xx

x

−

+

−

−

= −−

−−

Denominatorfactored: −−

+

−

−

= −−

−+

=+ −

+

1

1

3

2

87

21

12

1

x

x

x

x

xx

xx

x

()()

LCD( )( )

()(() ()()

()()

x x

x

xx x

x

xx x

−⋅−

+

−+ −⋅

−

=+ −⋅−−

2 21

1

123

2

128 77

21

22 13 187

252 23

()()

()()()

xx

xxxx x

xx

−+

−−−+=− −

−+− xxxx

xx x

2

2

387

8287

−=−−

−−+=−−

++ −++−

=−

=−

xx xx

x

x

22

2

82 82

09

03 ()(xx

xx

+

−= +=

3

30 30

)

++ −−

=

33 33

3

xxx=− 3

5.^41
1

5

1

x 24

x

x

xx

+

−

+ −

−

=

Using the fact that 1 − x = −(1 − x) allows us to write the second denom-

inator the same as the first.

41

1

5

1

24

41

1

5

1

24

x

x

x

xx

x

x

x

xx

x

+

−

+ −

−−

=

+

−

+−−

−

==

()

() LCD (()

() ()()()

x

xx x

x

xx x

x

xx

−

−⋅ +

−

+−⋅−−

−

=−⋅

1

1 41

1

1 5

1

1 24

xx

xx xx x

xx xx x

()()()()

()()(

41 5241

41 524

−+−−=−

+− −= − 1 1)