Simple fraction:

\[
   x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
\]

Formula with fractions:
\[
   \varphi_0(t)
   =
   \varphi_2(t)
   \int \frac{\varphi_1(t) q(t)}{W(t)}~dt
   -
   \varphi_1(t)
   \int \frac{\varphi_2(t) q(t)}{W(t)}~dt
\]

Fractions in matrices:   
\[
   A
   =
   \begin{pmatrix}
     \frac{1}{\sqrt{2}}
     &
     -\frac{1}{\sqrt{2}}
     \\     
     \frac{1}{\sqrt{2}}
     &
     \frac{1}{\sqrt{2}}
     \\
   \end{pmatrix}
\]

Increase size with $\backslash$displaystyle:
\[
   A
   =
   \begin{pmatrix}
     \displaystyle \frac{1}{\sqrt{2}}
     &
     \displaystyle -\frac{1}{\sqrt{2}}
     \\     
     \displaystyle \frac{1}{\sqrt{2}}
     &
     \displaystyle \frac{1}{\sqrt{2}}
     \\
   \end{pmatrix}
\]


$\overset{\displaystyle Max}{v \in X}$


$_{b}^{a}$

$\stackrel{a}{b}$

$\overline{\Omega}$

$\underline{W}$


$\overset{\circ}{\Omega}$

$\underset{\sim}W$

$\sideset{_1^2}{_3^4}\prod$