$$ \begin{aligned} \frac{3}{x}+2+\frac{4}{x}+3 &= \frac{7}{x}+6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}+x\cdot2+x\cdot\frac{4}{x}+x\cdot3 &= x\cdot\frac{7}{x}+x\cdot6&& \text{cancel out the denominators} \\[1 em]3+2x+4+3x &= 7+6x&& \text{simplify left and right hand side} \\[1 em]5x+7 &= 6x+7&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]5x-6x &= 7-7&& \text{simplify left and right hand side} \\[1 em]-x &= 0&& \text{ divide both sides by $ -1 $ } \\[1 em]x &= \frac{0}{-1}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

This page was created using