我怎样才能修复 align* 环境中这个过满的 hbox?

我怎样才能修复 align* 环境中这个过满的 hbox?

我有一个 align* 环境,其中包含一些方程式和对齐方式。但由于方程式太长,它给出了 overfull hbox 错误。我该如何解决这个问题?

\begin{align*}
     F_k & = F_{k - 1} + F_{k - 2} & \text{by the definition of the sequence}\\
     & = {\cfrac {1}{\sqrt {5}}}\left({\cfrac {1+{\sqrt {5}}}{2}}\right)^{k-2}-{\cfrac {1}{\sqrt {5}}}\left({\cfrac {1-{\sqrt {5}}}{2}}\right)^{k-2} + {\cfrac {1}{\sqrt {5}}}\left({\cfrac {1+{\sqrt {5}}}{2}}\right)^{k-1}-{\cfrac {1}{\sqrt {5}}}\left({\cfrac {1-{\sqrt {5}}}{2}}\right)^{k-1} & \text{by our inductive hypothesis}\\
     & = \frac{1}{\sqrt{5}}\left(\left(\left(\frac{1+\sqrt{5}}{2}\right)^{k-2}+\left(\frac{1+\sqrt{5}}{2}\right)^{k-1}\right)-\left(\left(\frac{1-\sqrt{5}}{2}\right)^{k-2}+\left(\frac{1-\sqrt{5}}{2}\right)^{k-1}\right)\right) & \text{by algebra}\\
     & = \frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^{k-2}\left(1+\frac{1+\sqrt{5}}{2}\right)-\left(\frac{1-\sqrt{5}}{2}\right)^{k-2}\left(1+\frac{1-\sqrt{5}}{2}\right)\right) & \text{by more algebra}\\
     & = \frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^{k-2}\left(\frac{1+\sqrt{5}}{2}\right)^{2}-\left(\frac{1-\sqrt{5}}{2}\right)^{k-2}\left(\frac{1-\sqrt{5}}{2}\right)^{2}\right) & \text{even more algebra}\\
     & = {\cfrac {1}{\sqrt {5}}}\left({\cfrac {1+{\sqrt {5}}}{2}}\right)^{k}-{\cfrac {1}{\sqrt {5}}}\left({\cfrac {1-{\sqrt {5}}}{2}}\right)^{k} & \text{last bit of algebra}\\
\end{align*}

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