I need help finding the delta for a given epsilon. I tried to solve by using algebra but I hit a wall.

$\displaystyle f(x)=2-\frac{1}{x}\\0<|x-1|<\delta\\|f(x)-1|<0.1\\|(2-\frac{1}{x})-1|<0.1\\|2-\frac{1}{x}-1|<0.1\\|-\frac{1}{x}+1|<0.1\\|-1||\frac{1}{x}-1|<0.1\\|\frac{1}{x}-1|<0.1$