Final answer:
It is not possible to find an equation for the tangent line at x=1 for the function f(x) = x/(x-1) because the function is undefined at that point, creating a discontinuity and preventing the determination of a finite slope.
Step-by-step explanation:
The question is about the possibility of finding the equation of a tangent line for the function f(x) = x/(x-1) at a specific point. To find the equation of a tangent line at a point on a curve, we must find the slope at that point. This slope is given by the derivative of the function at that point. In the case of f(x) = x/(x-1), we can find the derivative using the quotient rule of differentiation.
However, this function has an issue at x=1 because the denominator becomes zero, causing a discontinuity. This means the function is not defined at x=1, so it is not possible to find a finite slope or an equation for the tangent at that point. When the derivative does not exist or is undefined at a point, as it is here due to division by zero, we cannot find a tangent line at that specific point because a tangent line requires a well-defined slope.