Correct Answer: Option B

Explanation

\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}\)

= \(\frac{A(x - 3) + B(x - 2)}{(x - 2)(x - 3)}\)

\(\implies 5x - 12 = Ax - 3A + Bx - 2B\)

\(A + B = 5 ... (i)\)

\(-(3A + 2B) = -12 \implies 3A + 2B = 12 ... (ii)\)

From (i), \(A = 5 - B\)

\(3(5 - B) + 2B = 12\)

\(15 - 3B + 2B = 12 \implies B = 3\)

\(A + 3 = 5 \implies A = 2\)

\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{2}{x - 2} + \frac{3}{x - 3}\)

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