Using the formula [f(a+h)-f(a-h)]/2h = f prime of a, prove that

[f(a+h) - 2f(a) + f(a-h)]/h^2 = f double prime of a.

I get [f(a+h) - 2f(a) + f(a-h)]/2h^2

Could someone show me the proof of this? It's driving me crazy.

My work

[[2f(a+h) - 2f(a)] - [f(a+h) - f(a-h)]]/2h/h = the above (I assume incorrect) answer