\(A=\dfrac{\sqrt{x}+2+\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}:\dfrac{3\sqrt{x}+6-\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}\left(x\ge0\right)\\ A=\dfrac{2\sqrt{x}+3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}{2\sqrt{x}+3}=\dfrac{\sqrt{x}+3}{\sqrt{x}+1}\\ B=\dfrac{2\sqrt{x}-6-x-\sqrt{x}+x-\sqrt{x}+6}{\sqrt{x}\left(\sqrt{x}-3\right)}\\ B=\dfrac{0}{\sqrt{x}\left(\sqrt{x}-3\right)}=0\\ C=\dfrac{\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{\sqrt{x}-2+x+\sqrt{x}+2-\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\\ C=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\sqrt{x}}\\ C=\dfrac{2\left(\sqrt{x}+1\right)}{\sqrt{x}+2}\)
