INTRODUCTORY EXERCISES - Symbol Manipulation

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

  
 



 (a) 2(sqrt(2)) - (sqrt(2))	Where "sqrt" means the square root of
           ----------
                3

 (b) (t/4) - (7x/3) + (1/9)

 (c)  11  +    3
     ----   -------
      3x    (x - 2)

 (d) 3x - (20/x) - (5/4x2)

 (e)    1     -  1
     -------    ---
     (x + h)     x

 (a) 2(sqrt(2)) - (sqrt(2))    sqrt(2)
           ----------       =  -------
                3                 3


 (b) (t/4) - (7x/3) + (1/9) = (9t/36) - (84x/36) + (4/36)
                            = (9t - 84x + 4) / 36


 (c)  11       3       11(x - 2)       3(3x)
     ---- + ------- = -----------  +  ---------
      3x    (x - 2)   3x(x - 2)       3x(x - 2)
   
                       11(x - 2) + 3(3x)
                    = -------------------
                         3x(x - 2)
 
                        20x - 22
                    = ----------------
                         9x2 - 6x


 (d) 3x - (20/x) - (5/4x2) = 12x3 / 4x2 - (80x / 4x2) - (5/4x2)
                          = (12x3 - 80x - 5) / 4x2

 (e)    1     -  1        x           (x + h)
     -------    --- = ----------- - ------------
     (x + h)     x     x(x + h)      x(x + h)

                       x - (x + h)
                    = ------------
                       x2 + xh

                         -h
                    =  -----------
                        x2 + xh