$$ \begin{aligned} \frac{\frac{9}{10}}{x} &= \frac{6}{10}&& \text{multiply ALL terms by } \color{blue}{ x\cdot10 }. \\[1 em]x\cdot10 \cdot \frac{\frac{9}{10}}{x} &= x\cdot10\cdot\frac{6}{10}&& \text{cancel out the denominators} \\[1 em]9 &= 6x&& \text{ swap the left and right side of the equation } \\[1 em]6x &= 9&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{9}{6}&& \\[1 em]x &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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