$$ \begin{aligned} -\frac{1}{x^2}+\frac{2}{x^3} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2x^3 }. \\[1 em]-x^2x^3\cdot\frac{1}{x^2}+x^2x^3\cdot\frac{2}{x^3} &= x^2x^3\cdot0&& \text{cancel out the denominators} \\[1 em]-\frac{1}{x^1}+\frac{2}{x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1x^2 }. \\[1 em]-x^1x^2\cdot\frac{1}{x^1}+x^1x^2\cdot\frac{2}{x^2} &= x^1x^2\cdot0&& \text{cancel out the denominators} \\[1 em]-1+\frac{2}{x^1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]-x^1\cdot1+x^1\cdot\frac{2}{x^1} &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]-x+2 &= 0&& \text{ move the constants to the right } \\[1 em]-x &= -2&& \text{switch signs on both sides} \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

This page was created using