BECE Mathematics 2012 Paper

Concept:To subtract algebraic fractions, first write them with a common denominator.Explanation:The denominators are $4$ and $3$, so the least common denominator is $12$.Rewrite the first fraction with denominator $12$:$$\frac{3x}{4} = \frac{3x \times 3}{4 \times 3} = \frac{9x}{12}$$Rewrite the second fraction with denominator $12$:$$\frac{x-y}{3} = \frac{(x-y) \times 4}{3 \times 4} = \frac{4x-4y}{12}$$Now subtract the two fractions:$$\frac{3x}{4}-\frac{x-y}{3} = \frac{9x}{12}-\frac{4x-4y}{12}$$Since the denominators are the same, subtract the numerators:$$= \frac{9x-(4x-4y)}{12} = \frac{9x-4x+4y}{12}$$$$= \frac{5x+4y}{12}$$This matches option C.Answer:C. $\frac{5x+4y}{12}$