Answer:
Consider,
a ∈ Q – {-1} and b ∈ Q – {-1} be the inverse of a.
a * b = e = b * a
a * b = e and b * a = e
a + b + ab = 0 and b + a + ba = 0
b (1 + a) = – a Q – {-1}
b = -a/1 + a Q – {-1} [because a not equal to -1]
Hence, -a/1 + a is the inverse of a ∈ Q – {-1}