Question

Find the equation of the tangent line to the curve y=(x+1)/(x-1) at the point (2,3)? CAn anyone help me please?

Answer 1

take the derivative

[(x+1)'(x-1) -(x+1)(x-1)' ]/(x-1)^2
[x-1 - x -1]/(x-1)^2
-2/(x-1)^2

so plug in your point
y'(2) = -2/(2-1)^2 = -2/1^2 = -2
so thats your slope

now use equation of a line
y=mx+b
3 = -2(2) + b
3 = -4 + b
so b = 7

thus the equation of the tangent line is
y = -2x + 7