Find the least common denominator of $\frac{\frac{4}{(x+2)^{2}}-5 x}{\frac{7}{x(x+2)}}$ A) $x(x+2)$ B $x^{2}(x+2)^{2}$ C) $x(x+2)^{2}$ (D) $(x+2)^{2}$

Step 1 ：Identify the fractions in the expression, which are \(\frac{4}{(x+2)^{2}}\) and \(\frac{7}{x(x+2)}\).

Step 2 ：Identify the denominators of these fractions, which are \((x+2)^{2}\) and \(x(x+2)\).

Step 3 ：Find the least common multiple (LCM) of these two expressions. The LCM of \((x+2)^{2}\) and \(x(x+2)\) is \(x(x+2)^{2}\), because \((x+2)^{2}\) is a multiple of itself and \(x(x+2)\) is a multiple of \(x(x+2)^{2}\).

Step 4 ：Thus, the least common denominator (LCD) of the expression \(\frac{\frac{4}{(x+2)^{2}}-5 x}{\frac{7}{x(x+2)}}\) is \(x(x+2)^{2}\).

Step 5 ：\(\boxed{x(x+2)^{2}}\) is the final answer.