Final answer:
The simplified form of the rational expression (8x)/(72x^(2)-8x) is 1/(9x - 1). This is achieved by factoring out common terms and cancelling them. The expression is undefined for x = 0 or 1/9.
Step-by-step explanation:
To simplify the rational expression (8x)/(72x^(2)-8x), we need to first factor out common terms in the numerator and the denominator.
So, 8x in the numerator can be written as 8x. And the denominator can be factored as 8x(9x - 1).
Now, our expression becomes (8x)/(8x(9x - 1)). The common factor of 8x can be removed from both the numerator and the denominator.
After removing the common factor, our expression simplifies to 1/(9x - 1).
Note: the expression is undefined for values of x that make the denominator zero. Therefore, x cannot be 0 or 1/9.
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