Correct Answer: Option D

Explanation

\(\frac{11x + 2}{6x^2 - x - 1}\) = \(\frac{11x + 2}{(3x + 1)(2x - 1)}\)

= \(\frac{A}{3x + 1}\) + \(\frac{B}{2x - 1}\)

11x + 2 = A(2x - 1) + B(3x + 1)

put x = \(\frac{1}{2}\)

\(\frac{15}{2} = \frac{5}{2}B\)

B = 3.

put x = \(-\frac{1}{3}\)

\(-\frac{5}{3} = \frac{-5}{3}\)A \(\implies\) A = 1

∴ \(\frac{11x +2}{6x^2 - x - 1}\) = \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)

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