$$ \begin{aligned} \frac{1}{x}+1+\frac{1}{x}+2-(\frac{1}{x}+3)-(\frac{1}{x}+4) &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}+x\cdot1+x\cdot\frac{1}{x}+x\cdot2-x\cdot\frac{1}{x}+x\cdot3-x\cdot\frac{1}{x}+x\cdot4 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]1+x+1+2x-1+3x-1+4x &= 0&& \text{simplify left side} \\[1 em]1+x+1+2x-1+3x-1+4x &= 0&& \\[1 em]10x &= 0&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{0}{10}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

This page was created using