Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.

  • A 20
  • B 12
  • C -10
  • D -22
waec 2017furthermathematics

The correct answer is D. -22

Taking the LCM of the right hand side of the equation, we have

\(\frac{4(2x-3) - 2(x+5)}{(x+5)(2x-3)} = \frac{6x+m}{2x^{2}+7x-15}\)

Comparing the numerators, we have

\(4(2x-3) - 2(x+5) = 6x+m\)

\(8x-12-2x-10 = 6x -22 = 6x + m\)

\(\implies m = -22\)

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