1) \(\dfrac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\dfrac{4-a}{\sqrt{a}-2}=\dfrac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}+2}-\dfrac{\left(2-\sqrt{a}\right)\left(2 +\sqrt{a}\right)}{2-\sqrt{a}}\)
\(=\sqrt{a}+2-\left(2+\sqrt{a}\right)=\sqrt{a}+2-2-\sqrt{a=0}\)
2) \(\dfrac{9-a}{\sqrt{a}+3}-\dfrac{9-6\sqrt{a}+a}{\sqrt{a}-3}=\dfrac{\left(3+\sqrt{a}\right)\left(3-\sqrt{a}\right)}{\sqrt{a}+3}+\dfrac{\left(3-\sqrt{a}\right)^2}{3-\sqrt{a}}\)
\(=3-\sqrt{a}+3-\sqrt{a}=6-2\sqrt{a}\)
3) \(\dfrac{a+b+2\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a-b}{\sqrt{a}+\sqrt{b}}=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2}{\sqrt{a}+\sqrt{b}}-\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\)
\(=\sqrt{a}+\sqrt{b}-\left(\sqrt{a}-\sqrt{b}\right)=\sqrt{a}+\sqrt{b}-\sqrt{a}+\sqrt{b}=2\sqrt{b}\)
\(1,\dfrac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\dfrac{4-a}{\sqrt{a}-2}\left(a\ge0;a\ne4\right)\\ =\dfrac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}+2}-\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}-2}\\ =\sqrt{a}+2-\sqrt{a}-2=0\)
\(2,\dfrac{9-a}{\sqrt{a}+3}-\dfrac{9-6\sqrt{a}+a}{\sqrt{a}-3}\left(a\ge0;a\ne9\right)\\ =\dfrac{\left(3-\sqrt{a}\right)\left(3+\sqrt{a}\right)}{\sqrt{a}+3}-\dfrac{\left(\sqrt{a}-3\right)^2}{\sqrt{a}-3}\\ =3-\sqrt{a}-\left(\sqrt{a}-3\right)=6\)
