I don't understand how Newton find the Taylor expansion of $\frac{a^2}{b+x}$ by the following method :
**This screenshot is from : The method of fluxions and infinite series
Any idea ?
2026-03-30 12:23:41.1774873421
Newton's way of getting a Taylor expansion
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$$\begin{align}&aa\;&\mid& b+x\\&aa+\frac{aa}bx&\mid&\frac{aa}b\\ &------&--&----------\\ &0-\frac{aa}bx&\mid&\frac{aa}b-\frac{aax}{b^2}\\ &\;\;-\frac{aa}bx-\frac{aax^2}{b^2}&\mid&\\&------&--&----------\\&\frac{aax^2}{b^2}&\mid& \end{align}$$
and etc.
he thus gets
$$\frac{aa}{b+x}=\frac{aa}b-\frac{aax}{b^2}+\frac{aax^2}{b^3}-\ldots$$