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)