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

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\frac{2 * (x - 3)}{x + 3}$

Steps

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 $x^{2} - 6 x + 9$

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

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

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

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