Whats the inverse of y = 2x+1/x-1 ?

To find the inverse we're wanting to make x the subject. First start by multiplying both sides by (x-1), this gives us y(x-1) = 2x+1. 

Expand the brackets giving yx - y = 2x+1. 

Gather all the x components onto the same side:

yx - 2x = 1+y

now factorise the left hand side:

x(y-2) = 1+y

and make x the subject|:

x = 1+y/y-2

therefore the solution of the inverse is

f(x)^-1 = 1+x/ x-2

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