$$\frac{1}{x}+\frac{1}{x+1} = \frac{4}{x}$$

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

This page was created using