D = b^2 - 4ac = 3^2 - 4 * 5 * (-2) = 49
a1 = (-b + √D) / 2a = (-3 + 7) / 10 = 2/5
a2 = (-b - √D) / 2a = (-3 - 7) / 10 = -1
5a^2 + 3a - 2 = 5(a - 2/5)(a + 1) = (5a - 2)(a + 1)
a^2 - 1 = (a - 1)(a + 1)
(5a^2 + 3a - 2) / (a^2 - 1) = ((5a - 2)(a + 1)) / ((a - 1)(a + 1))
(5a - 2) / (a - 1)
Сокращённая дробь: (5a - 2) / (a - 1)
Или,
как вариант