If a2 + b2 + 2b + 4a + 5 = 0, then the value of a - ba + b\, is?

Answer: Option C

$$\begin{array}{rl}& a^2+b^2+2b+4a+5=0\\ & \Rightarrow a^2+b^2+2b+4a+4+1=0\\ & \Rightarrow a^2+4a+4+b^2+2b+1=0\\ & \Rightarrow {\left(a+2\right)}^2+{\left(b+1\right)}^2=0\\ & a+2=0\Rightarrow \text{ a}=-2\\ & b+1=0\Rightarrow b=-1\\ & \frac{a-b}{a+b}\Rightarrow \frac{-2+1}{-2-1}\\ & \Rightarrow \frac{-1}{-3}=\frac{1}{3}\end{array}$$