<s>[INST] Deriving equality with algebra? Can someone walk me through computation of the following equality?
$$\frac{1}{i}\int \frac{dz}{z(a + \frac{z + z^{-1}}{2})^2} = \frac{4}{i}\int \frac{zdz}{(z^2 + 2az + 1)^2}$$
I've gotten as far as:
$$\frac{4}{i}\int \frac{dz}{4z(a^2 + a(z + z^{-1}) + z^2 + z^{-2} + 2)}$$
but am unsure of how to proceed after this.
Thanks.
 [/INST] $$\frac{1}{i}\int\frac{dz}{z(a+\frac{z+z^{-1}}{2})^2}=\frac{1}{i}\int\frac{4dz}{z(2a+z+z^{-1})^2}=\frac{1}{i}\int\frac{4dz}{z\frac{(2az+z^2+1)^2}{z^2}}=\frac{4}{i}\int\frac{zdz}{(2az+z^2+1)^2}$$
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