\(If $f(x) = 2x + 3$ and $g(x) = 3x - 2$ find $\frac{f(g(f(2)))}{g(f(g(2)))}$. Express your answer in the form $\frac{a}{b}$.\)
Please help!
f(x) = 2x + 3 and g(x) = 3x - 2
f( g( f(2) ) ) = f( g( 7 ) ) = f( 19 ) = 41
g( f( g(2) ) ) = g( f( 4 ) ) = g( 11 ) = 31
And so...
\(\dfrac{f(\ g(\,f(2)\,)\ )}{g(\ f(\,g(2)\,)\ )}\ =\ \dfrac{41}{31}\)_
