Find the Tangent of y=1/(x-1) with Slope -1

[fiziksfun]

Find an equation for the tangent to the curve y=1/(x-1) that has slope -1.

 

[Winzer]

Ok you have y, you know that y'=-1. Is there a way you can find a point x where this happens?

 

[HallsofIvy]

If y= 1/(x-1)= (x-1)^-1, what is y'? (I hereby give you permission to use (xⁿ)'= nx^n-1!)