If $-6\leq a \leq -2$ and $3 \leq b \leq 5$, what is the greatest possible value of $\frac{a + 1/b}{a - 1/b}$? Express your answer as a common fraction.
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\(-6\leq a \leq -2 and 3 \leq b \leq 5\)
Note that [ a + 1/b ] / [ a - 1/b] = [ (a + b) / b ] [ (a - b) / b ] = [ a + b ] / [a - b ]
This will be maximimzed when a = -6 and b = 3
So [ a + b ] / [ a - b ] = [-6 + 3 ] / [ -6 - 3] = -3 / -9 = 1/3
