Question

6/(a^(2)+a-6) = 4/(a^(2)-9)

Answer 1

6/(a^2+a-6) = 4/(a^2-9).

6/(a-2)(a+3) = 4/(a-3)(a+3)
Multiply both sides by a+3:
6/(a-2) = 4/(a-3)
Cross multiply:
6a - 18 = 4a - 8
6a - 4a = -8 + 18
2a = 10
a = 5.