### 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 )