112 algebra De mystif ieD

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

10.^2
3

2

3

(^43242)
4
343424
4444
()()
()
xy yz ()()
xyz
xyyz
xyz
==x^331248
444
3168
444
34164
81
2
81
2
81
yyz
xyz
xyz
xyz
xy

= −−zzxyz
x
yz yz
x
84 2 1124 12 4 12 4
81
2
81
12
81
−−==⋅=
There are times in algebra, and especially in calculus, when we must write
a fraction as a product. Using the property^11
a
=a−, we can rewrite a fraction as
a product of the numerator and the denominator raised to the –1 power. Here
is the idea: numerator
denominator
=(numerator)(denominatorr)−^1.
EXAMPLES
Write the fraction as a product.
(^331)
x
= x−
4
3
431
x
x

• =+()−
  x
  y
  xy xy
  n
  m
  ==nm()−−^1 nm
  58
  23
  x 3 58233
  x
  − xx


• 
  

  =− + −
  ()
  ()()
  PRACTICE
  Write the fraction as a product.

  
  

1.^4

2

5

x

y

=

2.^23
12

xx

x

()

()

−

+

=

3. x
   y

=

4.^2
3 2

x

()y

=

5.^23
25

x

x

−

+

=

EXAMPLES

Write the fraction as a product.

EXAMPLES

Write the fraction as a product.

PRACTICE

Write the fraction as a product.

PRACTICE

Write the fraction as a product.