DOTS division
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Problem
Take any pair of two digit numbers $ ab $ and $ cd $ where, without loss of generality, $ ab> cd $. Form two 4 digit numbers $ abcd $ and $ cdab $ and calculate:
Student Solutions
We have received a very clearly explained solution to this, but unfortunately whoever sent it did not include their name. If it was you, let us know!
Let $ab=x$ and $cd=y$ (where $ab$ means $a$ as the tens digit, and $b$ as the ones digit, not $a$ times $b$).
(since $x> y$ we are not dividing by zero)