$$\frac{5}{x+1} = \frac{4}{3}$$

$$ \begin{aligned} \frac{5}{x+1} &= \frac{4}{3}&& \text{multiply ALL terms by } \color{blue}{ (x+1)\cdot3 }. \\[1 em](x+1)\cdot3\cdot\frac{5}{x+1} &= (x+1)\cdot3\cdot\frac{4}{3}&& \text{cancel out the denominators} \\[1 em]15 &= 4x+4&& \text{ swap the left and right side of the equation } \\[1 em]4x+4 &= 15&& \text{ move 4 to the right } \\[1 em]4x &= 15-4&& \\[1 em]4x &= 11&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{11}{4}&& \\[1 em] \end{aligned} $$

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