Find the equation of all lines having slope ` 1`that are tangents to the curve `y=1/(x-1), x!=1`.

Explanation

To find the equation of all lines having slope \(1\) that are tangents to the curve \(y = \frac{1}{x - 1}\) (where \(x \neq 1\)), we will follow these steps:

### Step 1: Find the derivative of the curve
The first step is to find the derivative of the function \(y = \frac{1}{x - 1}\) to determine the slope of the tangent at any point on the curve.

The derivative \(y'\) is calculated as follows:
\[
y = (x - 1)^{-1}
...