Find the equation of the tangent line to the curve y = 1/(x-1) that has a slope of -1.? w/ work please?

Answer 1

Priniciple: A tangent to a curve at a given point has the same slope as the derivitive of the curve at that point.

So y'= - 1/(x-1)^2
Find the value of x for which y'=-1
Go back to y= 1/(x-1) to find y for x from above.
Given the slope and a point coordinate, you can find the tangent line.