$$ \begin{aligned} \frac{1}{x-6} &= \frac{2}{x+7}&& \text{multiply ALL terms by } \color{blue}{ (x-6)(x+7) }. \\[1 em](x-6)(x+7)\cdot\frac{1}{x-6} &= (x-6)(x+7)\cdot\frac{2}{x+7}&& \text{cancel out the denominators} \\[1 em]x+7 &= 2x-12&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]x-2x &= -12-7&& \text{simplify left and right hand side} \\[1 em]-x &= -19&& \text{switch signs on both sides} \\[1 em]x &= 19&& \\[1 em] \end{aligned} $$

This page was created using