Re-arrange expression to transformation form

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$$\frac{6x-5}{3x+1}$$

How do you write this in the form

$$\frac{b}{x+c} + a$$

I know how to find a (2) by asymptote theory, but I don't know how to re-arrange to find B.

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$$\frac{6x-5}{3x+1}=\frac{2(3x+1)-7}{3x+1}=2-\frac7{3x+1}=2-\frac{\dfrac73}{x+\dfrac13}$$