Question 360833
Computing f(g(x))


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



{{{f(g(x))=(g(x)-1)/(g(x)-3)}}} Plug in {{{x=g(x)}}} on the right side.



{{{f(g(x))=((x-8)/(x-9)-1)/((x-8)/(x-9)-3)}}} Plug in {{{g(x)=(x-8)/(x-9)}}}



{{{f(g(x))=(x-8-(x-9))/(x-8-3(x-9))}}} Multiply EVERY term by the LCD {{{x-9}}} to clear out the fractions.



{{{f(g(x))=(x-8-x+9)/(x-8-3x+27)}}} Distribute.



{{{f(g(x))=1/(-2x+19)}}} Combine like terms.



I'll let you compute g(f(x))