INTRODUCTORY EXERCISES

(6) Write each fraction as a sum or difference.

  
 (a) (sqrt(3))(x) - 6	Where "sqrt" means the square root of
     ----------------
        (sqrt(3)) 

 (b)  3 + x2
     --------
        3

 (c)  4x - 5x2 - 2x5
      --------------
            x2

 (d) 3t2 + 5t
     ---------
        2t3 
  
 (e)  9(x + 1) - 7
     -------------   
       3(x + 1)

 (a) (sqrt(3))(x) - 6	  (sqrt(3))(x)  -     6
     ----------------  =  ------------    --------  
        (sqrt(3))           (sqrt(3))     (sqrt(3))

     = x  -    6
            --------
            (sqrt(3))
  Now, to rationalize (refer to HINT), multiply the top and bottom of
  the last term by (sqrt(3)):

   = x -   (6)(sqrt(3))          x  -  6(sqrt(3))
         ------------------  =         ----------
         (sqrt(3))(sqrt(3))                 3

   =  x - 2(sqrt(3))

 (b)  3 + x2       3  +  x2     1 + x2   
     --------  =  ---   ---  =     ---
        3          3     3          3

 (c)  4x - 5x2 - 2x5      4x  -  5x2  -  2x5
      --------------  =  ----   -----   ----
            x2            x2      x2      x2

   =  4  - 5 - 2x3
     ---          
      x

 (d) 3t2 + 5t       3t2  +  5t       3  +  5
     ---------  =  ----    ----  =  ---  ----
        2t3         2t3     2t3      2t   2t2

 (e)  9(x + 1)        7
     ---------- - ---------
      3(x + 1)     3(x + 1)
  
                 7
       = 3 - ---------
              3(x + 1)