If x - y + z = 0, then find the value of y^22xz - x^22yz - z^22xy?

Answer: Option A

$$\begin{array}{rl}& \frac{y^2}{2xz}-\frac{x^2}{2yz}-\frac{z^2}{2xy}\\ & \frac{y^3-x^3-z^3}{2xyz}......\left(1\right)\\ & x-y+z=0\\ & x+z=y\\ & \text{Cubing both side}\\ & {\left(x+z\right)}^3=y^3\\ & x^3+z^3+3\left(x+z\right)\left(x\right)\left(z\right)=y^3\\ & x^3+z^3+3\left(y\right)\left(x\right)\left(z\right)=y^3\\ & 3xyz=y^3-x^3-z^3\\ & \text{Put in equation }\left(1\right)\\ & \frac{3xyz}{2xyz}=\boxed{\frac{3}{2}}\end{array}$$