Simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex] is equal to 3/(x-6).
As given in the question,
Given complex fraction is [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]
Simplify the denominator by taking least common multiple,
[tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }\\\\\\= \frac{3}{\frac{x-4}{\frac{x-4-2}{x-4} } }\\\\\\= \frac{3(x-4)}{(x-6)(x-4)} \\\\\\=\frac{3}{x-6}[/tex]
Therefore, simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex] is equal to 3/(x-6).
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