Problem

Find the difference.
\[
\frac{8}{x^{2}-9 x}-\frac{1}{x^{2}-81}
\]
Enter the correct answer.

Answer

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Answer

Final Answer: The difference is \(\boxed{(x - 9)(7x + 72)}\).

Steps

Step 1 :The problem is asking for the difference between two fractions. To find the difference between two fractions, we need to find a common denominator.

Step 2 :The denominators of the two fractions are \(x^{2}-9 x\) and \(x^{2}-81\). We can factor these expressions to find a common denominator.

Step 3 :The common denominator will be the product of the unique factors of each denominator. So, the common denominator is \(x*(x - 9)^{2}*(x + 9)\).

Step 4 :Subtract the two fractions using the common denominator to get the difference. The difference is \((x - 9)*(7*x + 72)\).

Step 5 :Final Answer: The difference is \(\boxed{(x - 9)(7x + 72)}\).

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