$$ \begin{aligned} \frac{2x-1}{x+2} &= \frac{6}{5}&& \text{multiply ALL terms by } \color{blue}{ (x+2)\cdot5 }. \\[1 em](x+2)\cdot5 \cdot \frac{2x-1}{x+2} &= (x+2)\cdot5\cdot\frac{6}{5}&& \text{cancel out the denominators} \\[1 em]10x-5 &= 6x+12&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]10x-6x &= 12+5&& \text{simplify left and right hand side} \\[1 em]4x &= 17&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{17}{4}&& \\[1 em] \end{aligned} $$

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