Solve the equation
3/x^2+15x+56 = 2x/x-7 - x/x-8
Is
x^2+15x+56
all in the denominator?
I will assume it is.
Rewrite the right hand side with a common denominator.
3/(x^2+15x+56) =
[2x(x-8) -x(x-7)]/(x^2-15x+56)
= (x^2-9x)/(x^2-15x+56)
If the two denominators were the same, this would be easy to solve. The numnerators would have to be equal. Are you sure about the + sign in front of 15 on the left?
Unless you made a typing error, I don't see an easy solution other than graphing.