$$ \begin{aligned} 4x\cdot4-\frac{4}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]44x\cdot4-4\cdot\frac{4}{4} &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]64x-4 &= 0&& \text{ move the constants to the right } \\[1 em]64x &= 4&& \text{ divide both sides by $ 64 $ } \\[1 em]x &= \frac{4}{64}&& \\[1 em]x &= \frac{1}{16}&& \\[1 em] \end{aligned} $$

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