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Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} ...

Given that 6x+m2x2+7x154x+522x3, find the value of m

A.

20

B.

12

C.

-10

D.

-22

Correct answer is D

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

4(2x3)2(x+5)(x+5)(2x3)=6x+m2x2+7x15

Comparing the numerators, we have

4(2x3)2(x+5)=6x+m

8x122x10=6x22=6x+m

m=22