$$ \begin{aligned} 6-\frac{1}{y}-1 &= -\frac{2}{y}-2&& \text{multiply ALL terms by } \color{blue}{ y }. \\[1 em]y\cdot6-y\cdot\frac{1}{y}-y\cdot1 &= -y\cdot\frac{2}{y}-y\cdot2&& \text{cancel out the denominators} \\[1 em]6y-1-y &= -2-2y&& \text{simplify left and right hand side} \\[1 em]5y-1 &= -2y-2&& \text{move the $ \color{blue}{ -2y } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]5y+2y &= -2+1&& \text{simplify left and right hand side} \\[1 em]7y &= -1&& \text{ divide both sides by $ 7 $ } \\[1 em]y &= -\frac{1}{7}&& \\[1 em] \end{aligned} $$

This page was created using