+1450 If $a$ and $b$ are integers with $a > b$, what is the smallest possible positive value of $\frac{a+b}{a-b} + \frac{a-b}{a+b}$?
+128408 \($\frac{a+b}{a-b} + \frac{a-b}{a+b}$\)
[ (a + b)(a + b) + (a - b)(a - b) ] / [ a^2 - b^2 ] =
( [ a^2 + 2ab + b^2 + a^2 - 2ab +b^2 ] / [ a^2 - b^2] =
[ 2a^2 + 2b^2 ] / [ a^2 - b^2 ]
2 [ a^2 + b^2] / [ a^2 - b^2 ]
The smallest positive value, 2, is achieved when b = 0 and a is any positive integer
In every other case, [ a^2 + b^2] / [ a^2 - b^2 ] will be > 1 and the expression will be > 2
