\documentclass[a4paper,12pt]{report}
\usepackage{amsmath,amssymb}
\usepackage{xepersian}


\begin{document}
\begin{equation}\begin{split}

\Psi '(x)  &=    \frac{\mp f(x)f'''(x)}{f''(x)\sqrt{f'^2(x)-2f(x)f''(x)}}+    \\    
                &     \frac{f'''(x)\left[f'(x) \mp \sqrt{f'^2(x)-2f(x)f''(x)}\right]}{f''^2(x)}  

\end{split} \end{equation}
 
 
 
 \begin{equation}
 \begin{align}
 
 \Psi '(x)  &=\frac{\mp f(x)f'''(x)}{f''(x)\sqrt{f'^2(x)-2f(x)f''(x)}}   \\    
          &+  \frac{f'''(x)\left[f'(x) \mp \sqrt{f'^2(x)-2f(x)f''(x)}\right]}{f''^2(x)}  
          
  \end{align}
 \end{equation}
 
 
\begin{equation}
\begin{align*}

\vert p_n f(x_n)\vert +1-q  &    \leq  \dfrac{\vert p_n f^2(x_n)+f(x_n) \vert -\vert f(q_n)\vert}{\vert f(x_n) \vert} \nonumber \\ 

   &\leq \vert \dfrac{ p_n  f^2(x_n)+ f(x_n)- f(q_n)}{f(x_n)}\vert  \\
 
    & \leq  \vert p_n f(x_n) \vert +1+ q  \nonumber
\end{align*}
\end{equation}
 
 
 \end{document}