$$\(\mathrm{g}(x)=\frac{3 x^{3}+8 x^{2}-3 x-6}{x(x+3)} \equiv A x+B+\frac{C}{x}+\frac{D}{x+3}\)$$ (a) Find the values of the constants $$\(A, B, C\)$$ and $$\(D\)$$. (5) A curve has equation $$\[ y=g(x) \quad x> 0 \]$$ Using the answer to part (a), (b) find $$\(\mathrm{g}^{\prime}(x)\)$$. (2) (c) Hence, explain why $$\(\mathrm{g}^{\prime}(x)> 3\)$$ for all values of $$\(x\)$$ in the domain of $$\(g\)$$. (1)

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