Question:
For $y=\frac{x-4}{5x-10}$ and $x\neq 2$, what is the value of $y$ that is not attainable? Express your answer as a common fraction.

Answer:
First we multiply both sides by $5x-10$ which gives \[ x-4=(5x-10)y=5xy-10y \]We can rearrange to $-4+10y=x(5y-1)$. When $5y-1=0$ or $y=\frac15$, the left hand side is nonzero while the right hand side is zero, so $\boxed{\frac15}$ is unattainable.