## Finite Math and Applied Calculus (6th Edition)

$x=2-\frac{1}{x}$ $x-2=-\frac{1}{x}$ $x(x-2)=-1$ $x^{2}-2x+1=0$ $x^{2}-x-x+1=0$ $(x^{2}-x)+(-x+1)=0$ $x(x-1)-1(x-1)=0$ $(x-1)(x-1)=0$ $x-1=0$ $x=1$