$$ \begin{aligned} \frac{4}{5} &= \frac{16}{x+1}&& \text{multiply ALL terms by } \color{blue}{ 5(x+1) }. \\[1 em]5(x+1)\cdot\frac{4}{5} &= 5(x+1)\cdot\frac{16}{x+1}&& \text{cancel out the denominators} \\[1 em]4x+4 &= 80&& \text{ move 4 to the right } \\[1 em]4x &= 80-4&& \\[1 em]4x &= 76&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{76}{4}&& \\[1 em]x &= 19&& \\[1 em] \end{aligned} $$

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