Final answer:
To simplify the given expression, first rewrite 8x-72 and x^2-9x as 8(x-9) and x(x-9). You can then cancel out the (x-9) terms, resulting in the simplified expression x/24.
Step-by-step explanation:
To find the product and simplify the expression (x)/(8x-72)*(x^(2)-9x)/(3), you need to perform multiplication and simplify the resulting expression. Firstly though, you can observe that 8x-72 can be simplified to 8(x-9) and x^(2)-9x can be simplified to x(x-9). This simplification becomes:
(x)/(8*(x-9))*(x*(x-9))/(3) = x/(8 * 3).
After canceling out the (x-9) terms, your final simplified expression is x/24.
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