Express in partial fractions 11+26x2−x−1

Question 1 Report

Express in partial fractions $\frac{11 + 2}{6 x^{2} - x - 1}$

\frac{1}{3 x - 1}

\frac{3}{2 x + 1}

\frac{3}{3 x + 1}

\frac{1}{2 x - 1}

\frac{3}{3 x + 1}

\frac{1}{2 x - 1}

\frac{1}{3 x + 1}

\frac{3}{2 x - 1}

Answer Details

$\frac{11 + 2}{6 x^{2} - x - 1}$ = $\frac{11 + 2}{3 x + 1}$
= $\frac{A}{3 x + 1}$ + $\frac{B}{2 x - 1}$
11x = 2 = A(2x - 1) + B(3x + 1)
put x = $\frac{1}{2}$
= - $\frac{- 5}{3}$
= - $\frac{- 5}{3}$ A $\to$ A = 1
∴ $\frac{11 x + 2}{6 x^{2} - x - 1}$ = $\frac{1}{3 x + 1}$ + $\frac{3}{2 x - 1}$

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Algebraic Fractions

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