Using componendo and dividendo, find the value of x, given \(\frac{{\sqrt {3{\rm{x\;}} + {\rm{\;}}4} {\rm{\;}} + {\rm{\;}}\sqrt {3{\rm{x}}\; -\; 5} }}{{\sqrt {3{\rm{x\;}} + {\rm{\;}}4{\rm{\;}}}\; - \;\sqrt {3{\rm{x}}\; - \;5} }}\) = 9.

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