Express in partial fractions \(\frac{11x + 2}{6x^2 - x - 1}\)
A. \(\frac{1}{3x - 1}\) + \(\frac{3}{2x + 1}\)
B. \(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
C. \(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
D. \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
Correct Answer: 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 +Â 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
∴ \(\frac{11x +2}{6x^2 - x - 1}\) = \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
