Answer
$y=\frac{1}{2}, y=\frac{7}{6}$
Work Step by Step
$(\frac{y}{y-1})^{2}=6(\frac{y}{y-1})+7$
Simplify
$\frac{y^{2}}{(y-1)^{2}}=\frac{6}{y-1}+7$
Put everything on the left side
$\frac{y^{2}}{(y-1)^{2}}-\frac{6}{y-1}-7=0$
Add them
$\frac{y^{2}-6y(y-1)-7(y-1)(y-1)}{(y-1)^{2}}=0$
Multiply both side by $(y-1)^{2}$
${y^{2}-6y(y-1)-7(y-1)(y-1)}=0$
Simplify
$12y^{2}-20y+7=0$
Use quadratic equation
$\Delta= 20^{2}-7*12*4=64$
$\frac{20+\sqrt 64}{24}=\frac{7}{6}$
$\frac{20-\sqrt 64}{24}=\frac{1}{2}$