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I have the following expression $$ \frac{\left(-1\right)^{n} - 2 n - 1}{4 {\left(2 n + 1\right)}} $$ It clearly equals $$ \frac{\left(-1\right)^{n}}{4 {\left(2 n + 1\right)}} -\frac 1 4. $$

Is there anyway to make sage show this?