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
Correct Answer: Option D
Explanation
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)