Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction

Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction

Answer Details

To add fractions, we need to have a common denominator. In this case, the common denominator is \((x+3)(x-2)\). Therefore, we need to convert each fraction to have this denominator. \[\frac{2}{x+3} - \frac{1}{x-2} = \frac{2(x-2)}{(x+3)(x-2)} - \frac{(x+3)}{(x+3)(x-2)}\] Simplifying the above expression, we have: \[\frac{2(x-2) - (x+3)}{(x+3)(x-2)} = \frac{2x - 4 - x - 3}{(x+3)(x-2)} = \frac{x-7}{(x+3)(x-2)}\] Therefore, \(\frac{2}{x + 3} - \frac{1}{x - 2} = \boxed{\frac{x-7}{(x+3)(x-2)}}\). The correct option is (a).