Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 99

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

✔SOLUTIONS

1. ()()
   ()

(^51) (
51
51
51
51
23
2
23
21
xx 2
xx
xx
xx
++ xx
++
= ++
++
=++ ))(^31 − =+ 51 xx^22 + )

2. ()
   ()

(^7) () ()
7
77
9
3
x 93 6
x
==xx−

3. (2x − 5)^0 = 1


4. (x + 1)^11 (x + 1)^6 = (x + 1)^11 +^6 = (x + 1)^17


5. (x^2 − 1)(x^2 − 1)^3 = (x^2 − 1)^1 (x^2 − 1)^3 = (x^2 − 1)^1 +^3 = (x^2 − 1)^4


6. ((16x − 4)^5 )^2 = (16x − 4)(5)(2) = (16x − 4)^10

Adding/Subtracting Fractions

When adding fractions with variables in one or more denominators, the LCD

has each variable (or algebraic expression) to its highest power as a factor. For

example, the LCD for^1123112

x x yy

++ + is x^2 y^3 because the highest power on

x is 2, and the highest power on y is 3.

EXAMPLES

Identify the LCD and then find the sum or difference.

(^432)
xx
−
The LCD is x^2 because the highest power on x is 2.
43 43 22 4322432
xxxx
x
xx
x
x
x
x
−= −⋅=−= −
132 6
xy yz
−
The LCD includes xy, and z. Because 2 is the highest power on y, the LCD
also includes y^2. The LCD is xy^2 z. We multiply the first fraction by z
z
and the
second fraction by xy
xy
.
132261361322613
xy yz xy
z
zyz
xy
xy
z
xyz
xy
xyz
−=⋅− ⋅ =−=z−−^6
2
xy
xyz
2
14 5
1
(^21)
x
()xx++()x

• 
  


• 
  

  EXAMPLES
  Identify the LCD and then find the sum or difference.
  EXAMPLES
  Identify the LCD and then find the sum or difference.