MODERATE EXERCISES - Symbol Manipulation

(1) Simplify. 

  (a)     2h 
        -------
        (h + 1)
     -------------
          (h)

 (b) x2(x + sqrt(7))    Where "sqrt" means the square root of
     ---------------
       2x(x4 + x3)

 (c) x(x - 3) (3 + 5x)
             ------------
             (4x(2x - 6))

 (d) (1/1+z) - 1
     ------------
          z
( Click On HINT To Get Some Help , Click On SOLUTION To See The Answer )

(2) Expand each product. 

 (a) (2x - 5)(x2 - x - 1)

 (b) (x2 - (sqrt(2))(x) + 1 )(x2 + (sqrt(2))(x) + 1 )
( HINT , SOLUTION )

(3) Factor and simplify. 

 (a) x2t2 - 2xt3

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

 (c) (x2 - 3x) + (2x - 6)
     --------------------
           (x - 3)
( HINT , SOLUTION )

(4) Write each sum or difference as a single fraction. 

 (a) 32 - 32 - 32 
          ----  ----
	    3     5

 (b)  - 20
    --  ---
     t   t2

 (c) 5k + x3
         ----
          2k

 (d)    14    +   9
     --------   --------
     (2x - 3)   (2x + 3)

 (e)  2  +    5    -     3
     ---   -------   -------
      x     x - 1     x2 - x
( HINT , SOLUTION )

(5) Rewrite each fraction as a sum or difference. 

 (a) t2 - st
    ----------
       40t 
   
 (b) ky + (k - 1)x
    ---------------
          xy

 (c)  -7 + (x/2)
     ------------
          x
( HINT , SOLUTION )

(6) Solve the following equations. 

 (a) kx(k - x) = 0
   
 (b) 3x(3x + sqrt(2)) = 0
          
 (c) cx = cx(x + 0.5)

 (d) (2/3)(7x - )(x + 0.21) = 0
( HINT , SOLUTION )
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