Home » Express in partial fractions (frac{11x + 2}{6x^2 – x – 1})

Express in partial fractions (frac{11x + 2}{6x^2 – x – 1})

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})

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