$$ \begin{aligned} \frac{708+x}{727+x} &= 975&& \text{multiply ALL terms by } \color{blue}{ 727+x }. \\[1 em](727+x)\frac{708+x}{727+x} &= (727+x)\cdot975&& \text{cancel out the denominators} \\[1 em]708+x &= 975x+708825&& \text{move the $ \color{blue}{ 975x } $ to the left side and $ \color{blue}{ 708 }$ to the right} \\[1 em]x-975x &= 708825-708&& \text{simplify left and right hand side} \\[1 em]-974x &= 708117&& \text{ divide both sides by $ -974 $ } \\[1 em]x &= -\frac{708117}{974}&& \\[1 em] \end{aligned} $$

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