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

Further Mathematics
WAEC 2018

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. \(\frac{-1}{2(x - 2)} + \frac{8x}{2(x - 2)^{2}}\)
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Correct Answer: Option C
Explanation

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

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

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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WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
WAEC offline past questions - with all answers and explanations in one app - Download for free
WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
WAEC offline past questions - with all answers and explanations in one app - Download for free