a: \(=\dfrac{\sqrt{x}-3}{x-9}=\dfrac{1}{\sqrt{x}+3}\)
b: \(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}{\sqrt{x}-3}=\sqrt{x}-2\)
c: \(=6-2x-\left|x-3\right|\)
\(=6-2x-\left(3-x\right)\)
=6-2x-3+x=-x+3
e: \(=\sqrt{\dfrac{9}{4}}\cdot\left|x-1\right|+\dfrac{3}{2}-\left(x-2\right)\cdot\sqrt{\dfrac{25}{4}}\cdot\dfrac{x}{-x+2}\)
\(=\dfrac{3}{2}\cdot\left(x-1\right)+\dfrac{3}{2}-\dfrac{5}{2}\cdot\left(x-2\right)\cdot\dfrac{-x}{x-2}\)
\(=\dfrac{3}{2}x-\dfrac{3}{2}+\dfrac{3}{2}+\dfrac{5}{2}\cdot x\)
=4x
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