[tex]\displaystyle\\
\frac{3^{2012}+3^{2011}}{3^{2011}+3^{2010}} = \frac{5 \frac{1}{3}\cdot 3 \frac{1}{4}-\Big(6\frac{5}{11} \Big)^0}{4x} \\\\\\
\frac{3^{2010}(3^{2}+3^{1})}{3^{2010}(3^{1}+3^{0})} = \frac{\frac{16}{3}\cdot \frac{13}{4}-1}{4x}\\\\\\
\frac{3^{2}+3^{1}}{3^{1}+3^{0}} = \frac{\frac{208}{12}-1}{4x} \\\\\\
\frac{9+3}{3+1} = \frac{\frac{208}{12}-\frac{12}{12}}{4x} \\\\\\
\frac{12}{4} = \frac{\frac{208-12}{12}}{4x} \\\\\\
\frac{12}{4} = \frac{\frac{196}{12}}{4x}
[/tex]
[tex]\displaystyle\\
\frac{12^{^{(4}}}{4} = \frac{196^{^{(4}}}{12\cdot 4x} \\\\\\
\frac{3}{1} = \frac{49}{12x} \\\\
3\cdot 12x = 49 \cdot 1\\\\
36x=49\\\\
x= \frac{49}{36} = 1\frac{13}{36}[/tex]
