$$\frac{2}{x}+\frac{3}{4} = \frac{11}{12}$$

$$ \begin{aligned} \frac{2}{x}+\frac{3}{4} &= \frac{11}{12}&& \text{multiply ALL terms by } \color{blue}{ x\cdot4\cdot12 }. \\[1 em]x\cdot4\cdot12\cdot\frac{2}{x}+x\cdot4\cdot12\cdot\frac{3}{4} &= x\cdot4\cdot12\cdot\frac{11}{12}&& \text{cancel out the denominators} \\[1 em]96+36x &= 44x&& \text{move the $ \color{blue}{ 44x } $ to the left side and $ \color{blue}{ 96 }$ to the right} \\[1 em]36x-44x &= -96&& \text{simplify left side} \\[1 em]-8x &= -96&& \text{ divide both sides by $ -8 $ } \\[1 em]x &= \frac{-96}{-8}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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