HMMT 2017 A8

Consider all ordered pairs of integers $(a, b)$ such that $1 \leq a \leq b \leq 100$ and

$$\frac{(a+b)(a+b+1)}{a b}$$

is an integer. Among these pairs, find the one with largest value of $b$. If multiple pairs have this maximal value of $b$, choose the one with largest $a$. For example choose $(3,85)$ over $(2,85)$ over $(4,84)$. Note that your answer should be an ordered pair.