$$\frac{17}{5}f+\frac{213}{25} = \frac{14}{5}f+\frac{61}{10}$$

$$ \begin{aligned} \frac{17}{5}f+\frac{213}{25} &= \frac{14}{5}f+\frac{61}{10}&& \text{multiply ALL terms by } \color{blue}{ 50 }. \\[1 em]50 \cdot \frac{17}{5}f+50\cdot\frac{213}{25} &= 50 \cdot \frac{14}{5}f+50\cdot\frac{61}{10}&& \text{cancel out the denominators} \\[1 em]170f+426 &= 140f+305&& \text{move the $ \color{blue}{ 140f } $ to the left side and $ \color{blue}{ 426 }$ to the right} \\[1 em]170f-140f &= 305-426&& \text{simplify left and right hand side} \\[1 em]30f &= -121&& \text{ divide both sides by $ 30 $ } \\[1 em]f &= -\frac{121}{30}&& \\[1 em] \end{aligned} $$

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