If \( a+\alpha=1, \; b+\beta=2 \) and \( a f(x)+\alpha f\!\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, \; x\neq 0 \), then the value of the expression\( \displaystyle \frac{f(x) + f\left(\frac{1}{x}\right)}{x + \frac{1}{x}}\) is __________.
