1+\frac{8}{1+\frac{8}{1-\frac{8}{1+\frac{4}{1-\frac{4}{1-\frac{8}{x}}}}}}}=1993\\&amp;#10;\\&amp;#10;1) 1-\frac{4}{1-\frac{8}{x}}}=1-\frac{4x}{x-8}=\frac{-3x-8}{x-8}\\&amp;#10;2)1+\frac{4}{\frac{-3x-8}{x-8}}=\frac{-3x-8+4x-32}{-3x-8} = \frac{x-40}{-3x-8}\\&amp;#10;3)  1-\frac{8}{\frac{x-40}{-3x-8}}=\frac{x-40-8(-3x-8)}{x-40}=\frac{25x+24}{x-40}\\&amp;#10;4) 1+\frac{8}{\frac{25x+24}{x-40}}  =\frac{25x+24+8x-320}{25x+24} =\frac{33x-296}{25x+24}\\&amp;#10;5) 1+\frac{8}{\frac{33x-296}{25x+24}} = 1993\\&amp;#10; \frac{33x-296+200x+192}{33x-296}=1993\\&amp;#10; x=9&amp;#10;