Question 733559
Given expression is {{{(1+2/(x+2))/((1+8)/(x-4))) }}}.


Same as {{{(1+2/(x+2))*((x-4)/(1+8))}}}
= {{{(1*(x+2)/(x+2)+2/(x+2))*((x-4)/9)=((x+2+2)/(x+2))*((x-4)/9)}}}
={{{((x+4)/(x+2))*((x-4)/9)}}}
and a little bit of factoring is possible.
={{{((x+4)/(x+2))*((x-2)(x+2)/9)}}}
={{{((x+4)/cross((x+2)))*((x-2)*cross((x+2))/9)}}}
={{{(x+4)*((x-2)/9)}}}

From that, your final form can be
{{{highlight((x+4)(x-2)/9)}}}
OR
{{{highlight((x^2+2x-8)/9)}}}


The solution does not conform exactly to your listed generalized steps, but the solution is done in good order.