If 1/p + 1/q = 1p + q , then the value of p3 - q3 is?

Answer: Option D

$$\begin{array}{rl}& \frac{1}{p}+\frac{1}{q}=\frac{1}{p+q}\\ & \Rightarrow \frac{p+q}{pq}=\frac{1}{p+q}\\ & \Rightarrow {\left(p+q\right)}^2=pq\\ & \Rightarrow \left(p^2+q^2+2pq-pq\right)=0\\ & \Rightarrow \left(p^2+q^2+pq\right)=0\\ & \text{Multiply by }\left(p-q\right)\text{ both side}\\ & \Rightarrow \left(p-q\right)\left(p^2+q^2+pq\right)=\left(p-q\right)\times 0\\ & \Rightarrow p^3-q^3=0\end{array}$$