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Resolve \(\frac{3}{x^2 + x - 2}\) into partial fractions

Mathematics
JAMB 1992

Resolve \(\frac{3}{x^2 + x - 2}\) into partial fractions

  • A. \(\frac{1}{x - 1} - \frac{1}{x + 2}\)
  • B. \(\frac{1}{x + 1} + \frac{1}{x - 2}\)
  • C. \(\frac{1}{x + 1} - \frac{1}{x - 2}\)
  • D. \(\frac{1}{x - 2} + \frac{1}{x + 2}\)
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Correct Answer: Option A
Explanation

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

\(\frac{A}{x - 1}\) + \(\frac{B}{x + 2}\)

A(x + 2) + B(x - 1) = 3

when x = 1, 3A = 3 \(\to\) a = 1

when x = -2, -3B = 3 \(\to\) B = -1

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


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