If $S T=9, T U=5 x$, and $S U=12 x-12$, what is $T U ?$

Step 1 ：Given the equations: \(S T=9\), \(T U=5 x\), and \(S U=12 x-12\)

Step 2 ：We notice that the product of the first two equations (ST and TU) is equal to the third equation (SU).

Step 3 ：Therefore, we can find TU by dividing SU by ST.

Step 4 ：Substituting the given values, we get \(T U = \frac{S U}{S T} = \frac{12}{9} = 1.33\)

Step 5 ：Final Answer: \(T U = \boxed{1.33}\)