374 alGEbra De mystif ieD

EXAMPLES

Solve the equation.

x

xx

−

−−

(^1) =−
28
2
(^25)
This is in the form “fraction = fraction” so we cross-multiply.
51 28
52416
2416
2
2
2
()2( )
5
xxx
xxx
xx
−=−−−
−=−++
+−− +−−
+−=
+−=
+= −=
2416
2210
273
30
2
2
xx
xx
xx
xx
()() 0
270
−− 77   ++
=− =
=−
33
27 3
7
2
xx
x
Solve the equation.
4
2
14
xx^22
x
− xx

• 
  
  
  
  • = −
    −
    We begin by factoring each denominator so that we can find the LCD. After
    identifying the LCD, we will multiply each of the three terms by the LCD.
    4
    2
    14
    2
    2
    4
    2
    xx
    x
    xx
    xx
    xx
    xx
    xx
    ()
    LCD()
    (2)
    1()
    (
    −
  
  
  
  


• 
  
  
  
  • = −
    −
    =−
    − ⋅
    −
  
  
  
  


• −− ⋅ + = − ⋅ −
  −
  +− +=−
  +−−
  2
  1
  124
  2
  4214
  4 2
  )()
  1
  ()()
  x
  x
  xx
  x
  xx x
  xx 224
  24
  4
  2
  =−
  −+=−


• 
  

  x
  xx x
  x
  ()()

  
  


• 
  

  ++=
  ++=
  += +=
  4
  320
  210
  20 10
  2
  x
  xx
  xx
  xx
  −− −−

  
  

  22 11
  x −−= 21        x −
  EXAMPLES
  Solve the equation.
  EXAMPLES
  Solve the equation.