If x - a^2b + c + x - b^2c + a + x - c^2a + b = 4(a + b + c), then x = ?

Answer: Option A

$$\frac{x-a^2}{b+c}+\frac{x-b^2}{c+a}+\frac{x-c^2}{a+b}=4\left(a+b+c\right)$$
Note : In such type of question to save your valuable time assume values as per your need which make your calculation easier.
Assume a = 1, b = 0, c = 1
$$\begin{array}{rl}& \text{Make sure there will be no }\left(\frac{0}{0}\right)\text{ form}\\ & \therefore \frac{x-1}{1+0}+\frac{x-0}{1+1}+\frac{x-1}{1+0}=4\\ & \Rightarrow x-1+\frac{x}{2}+x-1=4\times 2\\ & \Rightarrow x+\frac{x}{2}+x=8+2\\ & \Rightarrow \frac{5x}{2}=10\\ & \Rightarrow x=4\\ & \text{Now put values in options take option}\\ & \left(\text{A}\right),{\left(a+b+c\right)}^2={\left(1+0+1\right)}^2=4\end{array}$$