Question 383091
{{{(fog)(x)=f(g(x))=f(y)=(y-3)/(y-1)}}}, with substitution {{{y=g(x)=(x-4)/(x-2)}}}
 
{{{((x-4)/(x-2)-3)/((x-4)/(x-2)-1)}}} | put on same denominator up and down
 
{{{ ((x-4-3*(x-2))/(x-2))/((x-4-(x-2))/(x-2))}}} |collect term in fractions
 
{{{((-2x+2)/(x-2))/((-2)/(x-2))}}} |use 1/(a/b)=b/a to "take up" the down fraction
 
{{{(-2x+2)/(x-2)*(x-2)/(-2)}}} |simplify terms up and down

{{{x-1}}}