Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.

  • A \(\frac{x}{2(x - 2)} - \frac{5}{(x - 2)^{2}}\)
  • B \(\frac{5}{(x - 2)} + \frac{x}{2(x - 2)^{2}}\)
  • C \(\frac{1}{2(x - 2)} + \frac{5x}{2(x- 2)^{2}}\)
  • D \(\frac{-1}{2(x - 2)} + \frac{8x}{2(x - 2)^{2}}\)
waec 2018furthermathematics

The correct answer is C. \(\frac{1}{2(x - 2)} + \frac{5x}{2(x- 2)^{2}}\)

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

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

Comparing, we have

\(3x - 1 = Ax - 2A + Bx  \implies -2A = -1;  A + B = 3\)

\(\therefore A = \frac{1}{2}; B = \frac{5}{2}\)

= \(\frac{1}{2(x - 2)} + \frac{5x}{2(x - 2)^{2}}\)

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