Question 359067
 
{{{f(x) = (x - 1)/(x - 3)}}} 
{{{g(x) = 3/(x - 1)}}}
{{{f(g)=(g-1)/(g-3)}}}
Let's simplify first.
{{{g-1=3/(x-1)-1}}}
{{{g-1=3/(x-1)-(x-1)/(x-1)}}}
{{{g-1=(3-(x-1))/(x-1)}}}
{{{g-1=(3-x+1)/(x-1)}}}
{{{g-1=(4-x)/(x-1)}}}
Similarly,
{{{g-3=3/(x-1)-3}}}
{{{g-3=3/(x-1)-(3(x-1))/(x-1)}}}
{{{g-3=(3-3(x-1))/(x-1)}}}
{{{g-3=(3-3x+3)/(x-1)}}}
{{{g-3=(6-3x)/(x-1)}}}

{{{g-3=(3(2-x))/(x-1)}}}

Put it all together,
{{{f(g)=(g-1)/(g-3)}}}
{{{f(g)=((4-x)/(x-1))/((3(2-x))/(x-1))}}}
{{{highlight(f(g)=(4-x)/(3(2-x)))}}}