\( \begin{array}{c}x^{(x-1)^{2}}=2 x+1 \\ x-\frac{1}{x}=?\end{array} \)
\(x-\frac{1}{x}=2-\frac{1}{2}=\frac{3}{2}\)
Step 1 :\(x^{(x-1)^{2}}-2x-1=0\)
Step 2 :\(u=x-1\)
Step 3 :\(x=u+1\)
Step 4 :\((u+1)^{u^{2}}-2(u+1)-1=0\)
Step 5 :\(u=1\)
Step 6 :\(x=2\)
Step 7 :\(x-\frac{1}{x}=2-\frac{1}{2}=\frac{3}{2}\)