In econometric, I have to use this formula to compute the inverse matrix

$\displaystyle (A\pm bc')^{-1}=A^{-1}\mp \left[\frac{1}{1\pm c'A^{-1}b}\right]A^{-1}bc'A^{-1}$

where A is a $\displaystyle n\times n$, symmetric, nonsingular matrix; b,c are n-column vectors, c' is transpose of c.

I used it but I did know how to prove this formula. I need your help.