ANSWERS:

2.3 x=4  
     ____  
      x 
   
    x²=4  
    x²-4
    (x-2)(x+2)
    x=-2 or +2

2.4 x-2= 8
        ____
         x
    
    x²-2x=8
    x²-2x-8
    (x-4)(x+2)
     x=4  x=-2

2.5 x       6
   ____ = _____
   x-2     x-1

x(x-1)=6(x-2)
x²-x=6x-12
x²-x=6x-12
x²-x-6x+12
x²-7x+12
(x-4)(x-3)
x=4 x=3
 
2.6 x+2     3       1
   _____ - ____ = _____ 
    x+1    x-2     x+1 
  
  (x+2)(x-2)-3(x+1)=1(x-2)
  x²-4-3x-3=x-2
  x²-4x-7+2
  x²-4x-5
  (x+1)(x-5)
  x not equal -1    x=5

2.7 a+1     -2       a+2
    ____ = _____ + _______
    a-1     a+2      1-a


    a+1     -2       a+2
    ____ = _____ - _______
    a-1     a+2      a-1
 
   (a+1)(a+2)=-2(a-1)-(a+2)(a+2)
   a²+3a+2=-2a+2-(a²+4a+4)
   a²+3a+2=-2a+2-a²-4a-4
   a²+3a+2=-a²-6a-2
   2a²+9a+4
   (2a+1) (a+4)
    a= - 1     a=-4
        ___
         2      

2.8       6     x+2     x+3     2x-2
    1  + ___ + _____ = _____ + _______
         x+1    x+1     x-1     1-x²
                                     
 
          6     x+2     x+3     2x-2
    1  + ___ + _____ = _____ - _______
         x+1    x+1     x-1     x²-1

 
          6     x+2     x+3     2x-2
    1  + ___ + _____ = _____ - _______
         x+1    x+1     x-1   (x+1)(x-1) 
  
     
    1(x+1)(x-1)+6(x-1)+(x+2)(x-1)=(x+3)(x+1)-(2x-2)

    x²-1+6x-6+x²+x-2=x²+4x+33-2x+2

    7x-9=x²-2x+5
    
    x²-9x+14
    
    (x+7) (x-2)
     
    x=7  x=2 

2.9   2         2        1           3 
    ______  = _____ + ________ + __________
    x²+3x+2    1-x²    x²+3x+2     x²+x-2

     2       -(2)        1           3 
    ______  = _____ + ________ + __________
  (x+2)(x+1)  x²-1    (x+2)(x+1)  (x-1)(x+2)

    2       -(2)            1           3 
 ______  =  _____     +   ________ + __________
(x+2)(x+1) (x+1)(x-1)    (x+2)(x+1)  (x-1)(x+2)    

L.C.M.=(x+1)(x-1)(x+2)

  2(x-1)=-2(x+2)+1(x_1)+3(x+1)
      
  2x-2=-2x-4+x-1+3x+3

  2x-2=2x-2

  xER  ;x not equal -2 x not equal 1 

2.10  3              x+3 
    _____ + x + 5 = _____
      x               x

     3+x²+5x=x+3
     x²+5x+3=x+3
     x²+4x
     x(x+4)
    x not equal 0  x= -4