$$ \begin{aligned} \frac{3}{x}+2+\frac{4}{x}+3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}+x\cdot2+x\cdot\frac{4}{x}+x\cdot3 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]3+2x+4+3x &= 0&& \text{simplify left side} \\[1 em]5x+7 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= -7&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{7}{5}&& \\[1 em] \end{aligned} $$

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