Can someone help me solve the inverse of f(x)=2x/(x-2). This is what I have. y=2x/(x-2). Then x=2y/(y-2). Then x+2 =2y/y. But what do I do next?? I'm stuck. Please help

Question

Can someone help me solve the inverse of f(x)=2x/(x-2).  This is what I have. y=2x/(x-2). Then x=2y/(y-2). Then x+2 =2y/y. But what do I do next?? I'm stuck. Please help

anonymous · Answer

solve $x=\frac{2y}{y-2}$ for $y$

anonymous · Answer

first step is to multiply by $y-2$ to get rid of the annoying denominator and write 
$$x(y-2)=2y$$ 
second step is to multiply out on the left to get 
$$xy-2x=2y$$ 
can you take it from there?

anonymous · Answer

Thank you. You really helped. :)