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More formally, is the following statement true? Let $\alpha$ be between 0 and 1.

\begin{equation} \alpha\frac{(A_t - A_{t-1})}{A_{t-1}}\ + (1-\alpha)\frac{(B_t - B_{t-1})}{B_{t-1}}= \frac{(\alpha A_t + (1-\alpha)B_t)-(\alpha A_{t-1} + (1-\alpha)B_{t-1})}{(\alpha A_{t-1} + (1-\alpha)B_{t-1})} \end{equation}

If it is not true, is it possible to determine how much they differ by?

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    $\begingroup$ To investigate whether this is true, something you could do is just plug in some numbers and see what happens. $\endgroup$ – Minus One-Twelfth Jun 6 at 12:31
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    $\begingroup$ Yeah I see it now, thank you for reminding me! $\endgroup$ – yonderkens Jun 6 at 12:37

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