### INTRODUCTORY EXERCISES - Symbol Manipulation

(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 )