Here is a labeled equation \eqref{eq1}:
$$x+1\over\sqrt{1-x^2}\label{eq1}$$
and another Equation
$$\frac{1}{3}\cdot\sum_{i=1}^{n} x^{3}\nonumber$$
This is equation test
\begin{equation}
f(x)=\dfrac{ax^2+bx+c}{e^{x+2}}
\end{equation}
This is an alignment test:
\begin{align*}
x&= y_1 - y_2 +y_3 -y_5 +y_8-\dots\\
&= y(0) y'\; \text{by Axiom 1.} \\
&= \text{by Eq.\eqref{eq1}} \\
&= y'\times y^\frac{n}{2} \\
\end{align*}