$$\frac{x-7}{x+1} = 4$$

$$ \begin{aligned} \frac{x-7}{x+1} &= 4&& \text{multiply ALL terms by } \color{blue}{ x+1 }. \\[1 em](x+1)\frac{x-7}{x+1} &= (x+1)\cdot4&& \text{cancel out the denominators} \\[1 em]x-7 &= 4x+4&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]x-4x &= 4+7&& \text{simplify left and right hand side} \\[1 em]-3x &= 11&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= -\frac{11}{3}&& \\[1 em] \end{aligned} $$

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