If a + 1/a + 2 = 0 Then find the value of (a + 2) + 1/((a + 2)) .

If a + \(\frac{1}{a}\) + 2 = 0

it is possible only when a = -1

So put a = -1 in the required term =

(a + 2) +  \(\frac{1}{a + 2}\) = (-1 + 2) +  \(\frac{1}{-1 + 2}\) = 2