Two fractions are shown below.

\[\textrm{Fraction} \ A: \frac{10^a +1}{10^a +2} \qquad \textrm{Fraction} \ B: \frac{10^b + 1}{10^b + 2}\]

For what values of \(a\) and \(b\) will fraction A be greater than fraction B?

How might your thinking change if instead we had these two fractions?

\[\textrm{Fraction} \ C: \frac{10^c +1}{10^c -1} \qquad \textrm{Fraction} \ D: \frac{10^d + 1}{10^d -1}\]

For what values of \(c\) and \(d\) will fraction C be greater than fraction D?