Identity involving the hypergeometric function

Question

Let $n$ be an integers greater than one and $p,q$ be real numbers.How do I prove the following identity: \begin{equation} F_{2,1}\left[ \begin{array}{cc} \frac{3}{2} - n && 2-n \\ & \frac{5}{2} \end{array}; \left(\frac{q}{p}\right)^2 \right] = 3 p^3 \frac{-(p-q)(\frac{p+q}{p})^{2 n}(p+q(1-2 n)) + (p+q)(p-q (1-2 n))(\frac{p-q}{p})^{2 n}}{8(n-1)n(2n-1)(p-q)q^3(p+q)} \end{equation}