\documentclass[fleqn,a4paper]{report}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{xepersian}

\begin{document}

\[\frac{1}{p-a}\cdot \frac{p+\imath a}{p- \imath a}=\frac{p+\imath a}{p^2+a^2}=\frac{p}{p^2+a^2}+\imath\frac{a}{p^2+a^2}\]



\begin{alignat*}{4}
&p=0&\Longrightarrow& &-1&=-A\Longrightarrow  A=1\\
&p=1&\Longrightarrow &&4&=2B\Longrightarrow  B=2\\
&p=-1, p=2&\Longrightarrow& &C&=-3, D=-2\\
& &\Longrightarrow& &F(p)&=\frac{1}{p}+\frac{2}{p-1}-\frac{3p+2}{s^2+1}\\
& &\Longrightarrow &
&L^{-1}[F(p)]&=L^{-1}\left[\frac{1}{p}\right]+L^{-1}\left[\frac{2}{p-1}\right] \\
&&&& & \quad -L^{-1}\left[\frac{3p}{p^2+1}\right]-L^{-1}\left[\frac{2}{p^2+1}\right]\\
&&&& &=1+3e^t-3\cos t-2\sin t
\end{alignat*}

تفاوت کسرها را در زیر ببینید:

$\frac{1}{2}$

$\dfrac{1}{2}$

\[\frac{1}{2}\]
\end{document}