Let f(x)=\frac{x+a}{x+b} satisfy f(f(f(x)))=x for real numbers a, b. If the maximum value of a is \frac{p}{q}, where p, q are relatively prime integers, what is |p|+|q|?
Let f(x)=\frac{x+a}{x+b} satisfy f(f(f(x)))=x for real numbers a, b. If the maximum value of a is \frac{p}{q}, where p, q are relatively prime integers, what is |p|+|q|?