$$ \begin{aligned} \frac{40}{100} &= \frac{69575-x}{x}&& \text{multiply ALL terms by } \color{blue}{ 100x }. \\[1 em]100x\cdot\frac{40}{100} &= 100x \cdot \frac{69575-x}{x}&& \text{cancel out the denominators} \\[1 em]40x &= -100x+6957500&& \text{move the $ \color{blue}{ -100x } $ to the left side} \\[1 em]40x+100x &= 6957500&& \text{simplify left side} \\[1 em]140x &= 6957500&& \text{ divide both sides by $ 140 $ } \\[1 em]x &= \frac{6957500}{140}&& \\[1 em]x &= \frac{347875}{7}&& \\[1 em] \end{aligned} $$

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