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hint: use the first order expansion (1+x)^-1=1-x for x<<1

keep terms up to first order only

Here is what I get:

I multiplied 1-e^(-B*deltaE) by E1+E2e^(-B*deltaE) based on (1+x)^-1=1-x and I get E1+deltaE*e^(-B*deltaE) + E2*e^(-2B*deltaE), but it is not the answer

Help would be appreciated