I was helping some students today, quite successfully, until I came across this problem:
$$\begin{align} \ce{A &<=>[$k_+$][$k_-$] B + C} \\[5pt] \ce{C + D &->[$k_1$] E} \end{align}$$
The first equation is a fast process with forward and reverse rate constants $k_+$ and $k_-$, respectively. The second process is slow, with rate constant $k_1$.
The objective is to write down a rate law for the resulting equation:
$$\ce{A + D -> B + E}$$
The technique that had been working was to write down the rate for the slow process...
$$r = k_1[\ce{C}][\ce{D}]$$
Since $\ce{C}$ is a product in the fast reaction, which is an equilibrium equation, we also have:
$$k_+[\ce{A}]=k_-[\ce{B}][\ce{C}]$$
This is where things went awry, because the rate law that we seek is a function of $[\ce{A}]$ and $[\ce{D}]$ only. Considering the stoichiometry, it seemed appropriate to put $[\ce{B}]=[\ce{C}]$. This leads to the substitution $[\ce{C}]=(\frac{k_+}{k_-})^{1/2}[\ce{A}]^{1/2}$. The interface has declared the result to be invalid, so it must be an illegal maneuver. How, then, do I eliminate $[\ce{B}]$ and $[\ce{C}]$ and come up with the desired reaction rate law?