INTRODUCTORY EXERCISES - Symbol Manipulation

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(1) Simplify. Expand any products.

 (a) 4y - (6 - 3x + y)

 (b) (2 + 13/3)(9/52)
              
 (c) (4/x)-1  

 (d) 3 - (1/2)(-x2 + x + 2) - 5(1.2x2 - 2.7)

 (e) 2r2 + 4(2r)(100/r2)

 (f) -36(x - 1)(x + 2)
 
 (g) (2x - 1)2

( Click On HINT To Get Some Help, Click On SOLUTION To See The Answer )

(2) Factor. Simplify further where appropriate. For (d) and (e), indicate what values of the variable make the expression undefined.

 (a) 42t2 - 6yt - 96xt

 (b) x - 2x2

 (c) (5a + b)(a - b) - 11b(a - b)

 (d) y2 + y
     -------
      y + 1

 (e) 4x2 + 8x
     --------
        2x3 

( HINT , SOLUTION )

(3) Write each quotient as a product.

 
 (a)  a 
     ---
      x

 (b)  7(x2 + 3)
     ----------
        10x

 (c)    -11
     ----------
     (x4 + 1)2 

( SOLUTION )

(4) Write each product as a quotient.

  (a) 10(1/x)

 (b) (-3/4)x(x + 1)3

 (c) (-2/t)  -1   (3)
           ------
           (t + 9)

( SOLUTION )

(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

( HINT , SOLUTION )

(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)
  

( HINT , SOLUTION )

(7) Solve the following equations.

  
 (a) x(x + 3) = 0 

 (b) 2y = (1/2)y2 

 (c) (x - 2)(3x + 5) = 0

 (d) 3x(2x + 1)(x - 8) = 0

 (e) (x2 - 9x)(x + 4) = 0 
  

( HINT , SOLUTION )

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