$$ \begin{aligned} \frac{19}{w}+\frac{5}{w^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ ww^2 }. \\[1 em]ww^2\cdot\frac{19}{w}+ww^2\cdot\frac{5}{w^2} &= ww^2\cdot0&& \text{cancel out the denominators} \\[1 em]19+\frac{5}{w^1} &= 0&& \text{multiply ALL terms by } \color{blue}{ w^1 }. \\[1 em]w^1\cdot19+w^1\cdot\frac{5}{w^1} &= w^1\cdot0&& \text{cancel out the denominators} \\[1 em]19w+5 &= 0&& \text{ move the constants to the right } \\[1 em]19w &= -5&& \text{ divide both sides by $ 19 $ } \\[1 em]w &= -\frac{5}{19}&& \\[1 em] \end{aligned} $$

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