$$ \begin{aligned} \frac{6}{x} &= \frac{13}{x}-15&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{6}{x} &= x\cdot\frac{13}{x}-x\cdot15&& \text{cancel out the denominators} \\[1 em]6 &= 13-15x&& \text{ swap the left and right side of the equation } \\[1 em]13-15x &= 6&& \text{ move 13 to the right } \\[1 em]-15x &= 6-13&& \\[1 em]-15x &= -7&& \text{ divide both sides by $ -15 $ } \\[1 em]x &= \frac{-7}{-15}&& \\[1 em]x &= \frac{7}{15}&& \\[1 em] \end{aligned} $$

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