I was going through some old papers on CFT particularly, 'CONFORMAL COVARIANT CORRELATION FUNCTIONS - Ferrara and Parisi' where an integral identity is used to motivate shadow operator formalism in CFT.
I am looking for a derivation(hints for deriving) or atleast a verification of the following identity $$ \int d^4 t \dfrac{1}{(t-x)^{2 \alpha}}\dfrac{1}{(t-y)^{2 \beta}} \dfrac{1}{(t-z)^{2 \gamma}} = \dfrac{1}{(x-y)^{2 (2-\gamma)}} \dfrac{1}{(y-z)^{2 (2-\alpha)}} \dfrac{1}{(x-z)^{2 (2-\beta)}}$$ where, $\alpha + \beta + \gamma = 4$.
There is a generalization of this identity of general dimension d.