When x → x0, limf (x) and limg (x) = ∞, then why is limf (x) + G (x) = ∞ wrong when x → x0?

When x → x0, limf (x) and limg (x) = ∞, then why is limf (x) + G (x) = ∞ wrong when x → x0?

In contrast, let g (x) = - f (x), obviously satisfy the condition, but f (x) + G (x) ≡ 0, the limit is 0