+743 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.
+129881 Note that [a + 1/b ] / [a -1/b ] = [ (ab +1) / b ] / [ (ab -1) / b ] = (ab + 1) / (ab -1)
Note that ab will be negative and the numerator and denominator will always have an absolute value difference of 2
The smallest possible fraction results when a = -2 and b = 3 = -5/- 7 = 5/7
The function is maximized when a = -6 and b = 5....so....
(-6*5 + 1) / (-6*5 - 1) = -29 / -31 = 29 / 31
