\sqrt 7=2+\frac 1{1+\frac 1{1+\frac 1{1+\frac 1{\frac 1{\frac {\sqrt 7+1}3-1}}}}}}=2+\frac 1{1+\frac 1{1+\frac 1{1+\frac 1{\frac 3{\sqrt 7-2}}}}}=2+\frac 1{1+\frac 1{1+\frac 1{1+\frac 1{\frac {3(\sqrt 7+2)}3}}}}}=2+\frac 1{1+\frac 1{1+\frac 1{1+\frac 1{\sqrt 7+2}}}}}