As part of a derivation for a formula I was given the following:
$$\frac{xy}{A} = \frac{1}{bcK} + \frac{x+y}{bc} \quad\Rightarrow\quad \frac{A}{xy} = bcK - \frac{A(x+y)K}{xy}$$
Where $b$, $c$, and $K$ are all constants (I've replaced most chemistry symbols with something more readable). The idea here is that by varying $x$ or $y$, and measuring $A$, you are able to determine $K$ (equilibrium constant) from the slope.
I was told the rearrangement involved some less user friendly maths, so I made a few attempts with little success. How is this rearrangement done? And what is the "less user friendly maths" used in this situation?
\begin{align} \frac{xy}{A} & =\frac{1}{bcK} + \frac{x+y}{bc}\\ & = \frac{1+(x+y)K}{bcK} \\ \implies bcK &=\left(1+(x+y)K\right)\left(\frac{A}{xy}\right)\\ &=\frac{A}{xy}+{A(x+y)K\over xy}\\ \implies \frac{A}{xy} &= bcK - \frac{A(x+y)K}{xy}\end{align}