$$ \begin{aligned} x\cdot\frac{8}{9}+\frac{21}{19} &= \frac{139}{57}&& \text{multiply ALL terms by } \color{blue}{ 171 }. \\[1 em]171x\cdot\frac{8}{9}+171\cdot\frac{21}{19} &= 171\cdot\frac{139}{57}&& \text{cancel out the denominators} \\[1 em]152x+189 &= 417&& \text{ move 189 to the right } \\[1 em]152x &= 417-189&& \\[1 em]152x &= 228&& \text{ divide both sides by $ 152 $ } \\[1 em]x &= \frac{228}{152}&& \\[1 em]x &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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