Add or subtract and simplify each of the following expressions. Justify that each step of your process makes sense.

1. $\frac { 3 x } { x ^ { 2 } + 2 x + 1 } + \frac { 3 } { x ^ { 2 } + 2 x + 1 }$ 

   Hint (a):

   Because the denominators are the same, simply add the numerators.

2. $\frac { 3 } { x - 1 } - \frac { 2 } { x - 2 }$ 

   Hint (b):

   To get a common denominator:

   Multiply the first fraction by $\frac{x-1}{x-1}$

   and the second fraction by $\frac{x-2}{x-2}.$

   More Help (b):

   When subtracting, distribute the negative to all terms in the numerator of the second fraction.