SOLUTION: Given {{{f(x)=(x-3)/(x-1)}}} and {{{g(x)=(x-4)/(x-2)}}} Find (f o g)(x)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Given {{{f(x)=(x-3)/(x-1)}}} and {{{g(x)=(x-4)/(x-2)}}} Find (f o g)(x)      Log On


   

Question 383091: Given f%28x%29=%28x-3%29%2F%28x-1%29 and g%28x%29=%28x-4%29%2F%28x-2%29
Find (f o g)(x)
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
%28fog%29%28x%29=f%28g%28x%29%29=f%28y%29=%28y-3%29%2F%28y-1%29, with substitution y=g%28x%29=%28x-4%29%2F%28x-2%29

%28%28x-4%29%2F%28x-2%29-3%29%2F%28%28x-4%29%2F%28x-2%29-1%29 | put on same denominator up and down

+%28%28x-4-3%2A%28x-2%29%29%2F%28x-2%29%29%2F%28%28x-4-%28x-2%29%29%2F%28x-2%29%29 |collect term in fractions

%28%28-2x%2B2%29%2F%28x-2%29%29%2F%28%28-2%29%2F%28x-2%29%29 |use 1/(a/b)=b/a to "take up" the down fraction

%28-2x%2B2%29%2F%28x-2%29%2A%28x-2%29%2F%28-2%29 |simplify terms up and down
x-1