TxO Math Bowl 2024 - Team Contest - Problem 3

In \triangle TXO, points G and L are on sides TO and XO, respectively, and points E and B are on side TX with E closer to X. Cevians OB and XG intersect at P, and XG intersects transversal EL at Q. As well, BE = 3, TG = TB = XL = LO = 6, and EX = OG = 9. If the value of \frac{QX}{PG} can be expressed as \frac{a}{b}, where a and b are relatively prime, positive integers, compute a + b.