$$ \begin{aligned} x+\frac{1}{x}-1-x-\frac{1}{x}+1 &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ x\cdot6 }. \\[1 em]x\cdot6x+x\cdot6\cdot\frac{1}{x}-x\cdot6\cdot1-x\cdot6x-x\cdot6\cdot\frac{1}{x}+x\cdot6\cdot1 &= x\cdot6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]6x^2+6-6x-6x^2-6+6x &= 5x&& \text{simplify left side} \\[1 em]6x^2+6-6x-6x^2-6+6x &= 5x&& \\[1 em]0 &= 5x&& \text{ swap the left and right side of the equation } \\[1 em]5x &= 0&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{0}{5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

This page was created using