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

Assessment: WAEC SSCE - General Mathematics - 2013 (Objective) Subject: General Mathematics

Question 1 Report

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).
Read lesson note on Algebraic Fractions (WAEC)
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