a) $\dfrac{x-1}{x-5}=\dfrac{6}{7}$
$↔7(x-1)=6(x-5)$
$↔7x-7=6x-30$
$↔7x-7-6x+30=0$
$↔x+23=0$
$↔x=23$
b) $\dfrac{x^2}{6}=\dfrac{24}{25}$
$↔x^2=\dfrac{24}{25}.6=\dfrac{144}{25}$
\(↔\left[ \begin{array}{l}x=\dfrac{12}{5}\\x=-\dfrac{12}{5}\end{array} \right.\)