1. The problem is to divide the function $$f(x)=\frac{2x-1}{x-1}$$ into two functions $$u(x)$$ and $$v(x)$$ such that $$f(x) = \frac{u(x)}{v(x)}$$. 2. Observe the given function $$f(x) = \frac{2x - 1}{x - 1}$$. 3. We can simply assign the numerator to $$u(x)$$ and the denominator to $$v(x)$$: $$u(x) = 2x - 1$$ $$v(x) = x - 1$$ 4. This is a valid division since $$f(x) = \frac{u(x)}{v(x)} = \frac{2x - 1}{x - 1}$$. Thus, the functions are: $$u(x) = 2x - 1$$ $$v(x) = x - 1$$