\sqrt 7=2+\frac 1{1+\frac 1{1+\frac 1{\frac 1{\frac{\sqrt 7+1}2-1}}}}=2+\frac 1{1+\frac 1{1+\frac 1{\frac 2{\sqrt 7-1}}}}=2+\frac 1{1+\frac 1{1+\frac 1{\frac {2(\sqrt 7+1)}6}}}=2+\frac 1{1+\frac 1{1+\frac 1{\frac{\sqrt 7+1}3}}}