Algebraic manipulation question find inverse

Question

Could someone explain which algebraic manipulations is used to get the result on the right side of the red box.

In my opinion will $$ \frac {2}{x-2}={y-1}$$ lead to

$$ \frac {2}{y-1}+2={x}$$

So how do i get $$ \frac {1}{2 ({y-2})}+2={x}$$ ??

question in red

Answer 1

We get by multiplication by $$(x-2)$$:$$2=(x-2)(y-1)$$ and then dividing by $$y-1$$ so we get $$\frac{2}{y-1}=x-2$$ adding $$2$$ so we get $$\frac{2}{y-1}+2=x$$