If the rational expressions have a common factor, it is usually easier to add the terms using the standard method of first finding a common denominator. Find the sums of the following. First find equivalent fractions as shown in the example below. 

$\left. \begin{array} { c } { \frac { 5 } { x ^ { 2 } - 4 } - \frac { 2 } { x ^ { 2 } - x - 6 } } \\ { \frac { 5 } { ( x - 2 ) ( x + 2 ) } - \frac { 2 } { ( x - 3 ) ( x + 2 ) } } \\ { \frac { 5 ( x - 3 ) } { ( x - 2 ) ( x + 2 ) ( x - 3 ) } - \frac { 2 ( x - 2 ) } { ( x - 3 ) ( x + 2 ) ( x - 2 ) } } \end{array} \right.$ $\left. \begin{array} { c } { \frac { 5 x - 15 - 2 x + 4 } { ( x - 2 ) ( x + 2 ) ( x - 3 ) } } \\ { \frac { 7 x - 11 } { ( x - 2 ) ( x + 2 ) ( x - 3 ) } } \end{array} \right.$

1. $\frac { 2 x - 5 } { 6 } + \frac { x + 1 } { 8 }$ 

   Answer (a):

   $\frac{11x-17}{24}$

2. $\frac { x } { x ^ { 2 } + 2 x - 8 } + \frac { 2 } { x + 4 }$ 

   Answer (b):

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