Find the inverse of y = 2x+1/ x-1

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (x-1), giving us:y(x-1) = 2x+1now we need to expand the brackets:yx - y = 2x+1now gather all the x components on the same side:yx-2x = 1+ynow factorise the left hand side:x(y-2) = 1+ynow make x the subject, giving us:x = 1+y/ y-2therefore, the inverse is written in terms of x, which gives us:f(x)^-1 = 1+y/y-2