If $g(x) = 1-x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:

Given:

First, find $g(h(x))$:

Next, find $h(g(x))$:

Now, compute the ratio:

Let us evaluate the options:

• Option (A): $\frac{h(x)}{g(x)} = \frac{\frac{x}{x-1}}{1-x} = \frac{x}{-(x-1)^2} = \frac{-x}{(x-1)^2}$

This matches our computed ratio. Therefore, the correct option is (A).