If \(\alpha>0\) and \(\beta\) are the roots of the equation
\[
\sqrt{\frac{x-1}{x+2}}
+
\sqrt{\frac{x+2}{x-1}}
=
\frac{13}{6},
\]
then \(4\alpha-\beta=\)
Show Hint
For expressions of the form
\[
\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}},
\]
always substitute one term as \(t\) and the other automatically becomes \(\frac1t\).