2016/076) If a,,b,c are 3 unequal terms of AP then show that $\frac{b-c}{a-b}$ is rational.

proof
let $1^{st}$ term be p and difference d. Let a be $q^{th}$,  b be $r^{th}$,  c be $s^{th}$
so $a = p+(q-1)t$
$b= p+(r-1)t$
$c= p + (s-1)t$
hence $b-c = (r-s)t$
and $a-b = (q-r)t$
or  $\frac{b-c}{a-b} =  \frac{q-r}{r-s}$
as $q,r,s$ are intgers rhs is rational and hence the result