MODERATE EXERCISES - Symbol Manipulation

(3) Factor and simplify.

 (a) x2t2 - 2xt3

 (b)  9 (z - 2) +  9  (4 - z)
     ---          --- -------
      z            z    (6)

 (c) (x2 - 3x) + (2x - 6)
     --------------------
           (x - 3)

 (a) x2t2 - 2xt3
     xt2(x - 2t]

 (b)  9 (z - 2) +  9  (4 - z)     9  [(z - 2) + (4 - z)]
     ---          --- -------  = ---             ------
      z            z    (6)       z                 6

     = (9/z)[ 6(z - 2) + (4 - z) ]     9   (6z - 12 + 4 - z)  
             --------------------  =  ----                    
                     6                 6z                        
     = 3 (5z - 8)
      ---
       2z

(c)  (x2 - 3x) + (2x - 6)       x(x - 3) + 2(x - 3)
     --------------------  =   -------------------  
           (x - 3)                   (x - 3)
  
     = x + 2