The simplest value of 3 8 - 2 12 + 20 3 18 - 2 27 + 45 is:

Answer: Option B

$$\begin{array}{rl}& \text{Expression}\\ & =\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\ & =\frac{3\sqrt{2\times 2\times 2}-2\sqrt{2\times 2\times 3}+\sqrt{2\times 2\times 5}}{3\sqrt{3\times 3\times 2}-2\sqrt{3\times 3\times 3}+\sqrt{3\times 3\times 5}}\\ & =\frac{6\sqrt{2}-4\sqrt{3}+2\sqrt{5}}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}\\ & =\frac{2\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}{3\left(3\sqrt{2}-2\sqrt{3}+\sqrt{5}\right)}\\ & =\frac{2}{3}\end{array}$$