Problem

Simplify the expression: $\frac{(x-3)^{2}}{x} \div \frac{x^{2}-9}{2 x}=$

Solution

Step 1 :Rewrite the division as multiplication: \(\frac{(x-3)^{2}}{x} \times \frac{2 x}{x^{2}-9}\)

Step 2 :Simplify the expression \((x-3)^{2}\) to \(x^{2} - 6x + 9\)

Step 3 :Factor the expression \(x^{2}-9\) to \((x-3)(x+3)\)

Step 4 :Substitute these simplifications into the expression: \(\frac{x^{2} - 6x + 9}{x} \times \frac{2 x}{(x-3)(x+3)}\)

Step 5 :Simplify the expression to \(\frac{2*(x - 3)}{x + 3}\)

Step 6 :Final Answer: \(\boxed{\frac{2*(x - 3)}{x + 3}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/46252/

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