$$4 \cdot \frac{x}{x}+4 = \frac{3}{x}-1$$

$$ \begin{aligned} 4 \cdot \frac{x}{x}+4 &= \frac{3}{x}-1&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot4 \cdot \frac{x}{x}+x\cdot4 &= x\cdot\frac{3}{x}-x\cdot1&& \text{cancel out the denominators} \\[1 em]4x+4x &= 3-x&& \text{simplify left and right hand side} \\[1 em]8x &= -x+3&& \text{move the $ \color{blue}{ -x } $ to the left side} \\[1 em]8x+x &= 3&& \text{simplify left side} \\[1 em]9x &= 3&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{3}{9}&& \\[1 em]x &= \frac{1}{3}&& \\[1 em] \end{aligned} $$

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