Perform the indicated operation to simplify each of the following expressions. In some cases, factoring may help you simplify.

1. $\frac { ( x + 2 ) ( x - 3 ) } { ( x + 1 ) ( x - 4 ) } \cdot \frac { ( x + 1 ) } { x ( x + 2 ) }$ 

   Answer (a):

   $\frac{x-3}{x(x-4)}$

2. $\frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } - 4 } \cdot \frac { 4 } { x + 3 }$ 

   Hint (b):

   Factor the quadratic polynomials.

   More Help (b):

   $\frac{(x+2)(x+3)}{(x+2)(x-2)}\cdot\frac{4}{x+3}$

3. $\frac { 2 x } { x + 4 } + \frac { 8 } { x + 4 }$ 

   Hint (c):

   Factor after adding to see if there’s a Giant One you can remove.

   Answer (c):

   $2$

4. $\frac { x } { x + 1 } - \frac { 1 } { x + 1 }$ 

   Hint (d):

   Add the fractions.