$$ \begin{aligned} 1000 &= \frac{x+9}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot1000 &= x \cdot \frac{x+9}{x}&& \text{cancel out the denominators} \\[1 em]1000x &= x+9&& \text{move the $ \color{blue}{ x } $ to the left side} \\[1 em]1000x-x &= 9&& \text{simplify left side} \\[1 em]999x &= 9&& \text{ divide both sides by $ 999 $ } \\[1 em]x &= \frac{9}{999}&& \\[1 em]x &= \frac{1}{111}&& \\[1 em] \end{aligned} $$

This page was created using