21. The ratio of the radii of two circles is $3: 2$. Expressed in terms of $\pi$, what are the areas of the circles if the radius of the larger circle is $(2+\sqrt{x}) \mathrm{cm}$ and the radius of the smaller circle is $(2-\sqrt{x}) \mathrm{cm}, x \geq 0$ ? A larger circle: $\frac{x+3}{x+2}+\frac{x+11}{x^{2}-5 x-14}$; smaller circle: $\frac{1150}{625} \pi$ B larger circle: $\frac{54}{25} \pi$; smaller circle: $\frac{46}{25} \pi$ C larger circle: $\frac{144}{625} \pi$; smaller circle: $\frac{64}{625} \pi$ D larger circle: $\frac{144}{25} \pi$; smaller circle: $\frac{64}{25} \pi$

Step 1 ：Set up a proportion using the given ratio and the radii expressions: \(\frac{2+\sqrt{x}}{2-\sqrt{x}} = \frac{3}{2}\)

Step 2 ：Solve for x: \(x \approx 0.16\)

Step 3 ：Find the radii of both circles: Larger circle radius: \(2+\sqrt{x} \approx 2.4\) cm, Smaller circle radius: \(2-\sqrt{x} \approx 1.6\) cm

Step 4 ：Find the areas of both circles using the formula for the area of a circle, \(A = \pi r^2\): Larger circle area: \(5.76\pi\), Smaller circle area: \(2.56\pi\)

Step 5 ：Final Answer: The areas of the circles are \(\boxed{\frac{144}{25} \pi}\) for the larger circle and \(\boxed{\frac{64}{25} \pi}\) for the smaller circle.