$$\frac{12}{x+1} = \frac{x+4}{x+1}$$

$$ \begin{aligned} \frac{12}{x+1} &= \frac{x+4}{x+1}&& \text{multiply ALL terms by } \color{blue}{ x+1 }. \\[1 em](x+1)\cdot\frac{12}{x+1} &= (x+1)\frac{x+4}{x+1}&& \text{cancel out the denominators} \\[1 em]12 &= x+4&& \text{ swap the left and right side of the equation } \\[1 em]x+4 &= 12&& \text{ move 4 to the right } \\[1 em]x &= 12-4&& \\[1 em]x &= 8&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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