Ta có:
\(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}=\frac{x+2}{12^{12}}+\frac{x+2}{13^{13}}\)
\(\Rightarrow\left(x+2\right).\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}\right)=\left(x+2\right).\left(\frac{1}{12^{12}}+\frac{1}{13^{13}}\right)\)
Mà \(\frac{1}{10^{10}}+\frac{1}{11^{11}}\ne\frac{1}{12^{12}}+\frac{1}{13^{13}}\)
\(x+2=0\)
\(\Rightarrow x=-2\)
Vậy x=-2