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: 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})