When trying to approximate the behavior of a function in some particular limits, we can use things such as binomial approximations or Taylor expansions. For example, if I have the following formula $$\left(c+\frac{x}{y}\right)^5,$$ and I know that $\frac{x}{y}<<1$, I can use a Taylor expansion centered at $0$ using $\frac{x}{y}$ as a variable to approximate the behavior of the function as $\frac{x}{y}$ changes.
What if instead I have something like this: $$\left(\frac{c}{y}+\frac{x}{y}\right)^5$$ Now that "$c$" (which was some constant) has become $\frac{c}{y}$, which is dependent on $\frac{x}{y}$, I'm not sure I can employ the same strategy.
My question is, would it still be valid to approximate it the same way? $\frac{x}{y}$ is still very close to $0$ and maybe $\frac{c}{x}$ does not affect the function all that much.
Thank you!