$$ \begin{aligned} 2x+\frac{3}{5} &= x+2&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot2x+5\cdot\frac{3}{5} &= 5x+5\cdot2&& \text{cancel out the denominators} \\[1 em]10x+3 &= 5x+10&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]10x-5x &= 10-3&& \text{simplify left and right hand side} \\[1 em]5x &= 7&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{7}{5}&& \\[1 em] \end{aligned} $$

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