Question 214736
Remember that *[Tex \LARGE (f \circ g)(x)] is another way of saying {{{f(g(x))}}}. 




{{{f(x)=(x-1)/(x-3)}}} Start with the given function.



{{{f(g(x))=(3/(x-1)-1)/(3/(x-1)-3)}}} Plug in {{{g(x)=3/(x-1)}}}



Note: this involves replacing 'x' on the left side with {{{g(x)}}} and replacing each 'x' on the right side with {{{3/(x-1)}}}. 



{{{f(g(x))=(cross((x-1))(3/cross((x-1)))-1(x-1))/(cross((x-1))(3/cross((x-1)))-3(x-1))}}} Multiply EVERY term by the inner LCD {{{x-1}}} to clear out the inner fractions.



{{{f(g(x))=(3-(x-1))/(3-3(x-1))}}} Simplify



{{{f(g(x))=(3-x+1)/(3-3x+3)}}} Distribute



{{{f(g(x))=(-x+4)/(-3x+6)}}} Combine like terms.




So *[Tex \LARGE (f \circ g)(x)=\frac{-x+4}{-3x+6}]