Food for thought

## Problem

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?

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

For what values of $c$ and $d$ will fraction C be greater than fraction D?