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\begin{document}
\textit{Recreate the following expression in inline mode:}

$$\left(\frac{x^3}{3(x+1)^2}\right)^{\frac{1}{n}}$$

\textit{Recreate the following proof by using align:}

	The solution of $ax^2+bx+c=0$ where $a\neq 0$ is

	\begin{align}
		\frac{-b\pm \sqrt{d}}{2a}\text{ where }d=b^2-4ac
	\end{align}
	\begin{proof}
		We see that the equation is equivalent to
		\begin{align}
			ax^2+bx&=-c
			\intertext{Or equivalently}
			-\frac{c}{a}=x^2+\frac{b}{a}x&=x^2+2\frac{b}{2a}x
			\intertext{By adding $\left(\frac{b}{2a})\right)^2$ to both sides we get} 
			\left(\frac{b}{2a}\right)^2-\frac{c}{a}&=x^2+2\frac{b}{2a}+\left(\frac{b}{2a}\right)^2\\
			&=\left(x+\frac{b}{2a}\right)^2
			\intertext{By multiplying $4a^2$ to bot sides we get}
			b^2-4ac&=(2ax+b)^2
			\intertext{So}
			\pm \sqrt{b^2-4ac}&=2ax+b
			\intertext{And therefore}
			\frac{-b \pm \sqrt{b^2-4ac}}{2a}&=x
		\end{align}
	\end{proof}

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