Question

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Answer 1

$\frac{1}{z-d}-\frac{3zd}{z^{3}-d^{3}}=\frac{1}{z-d}-\frac{3zd}{(z-d)(z^{2}+zd+d^{2})}=\frac{z^{2}+zd+d^{2}-3zd}{(z-d)(z^{2}+zd+d^{2})}=\frac{z^{2}-2zd+d^{2}}{(z-d)(z^{2}+zd+d^{2})}=\frac{(z-d)^{2}}{(z-d)(z^{2}+zd+d^{2})}=\boxed{\frac{z-d}{z^{2}+zd+d^{2}}}$