$$\frac{10}{x+3}+\frac{10}{3} = 6$$

$$ \begin{aligned} \frac{10}{x+3}+\frac{10}{3} &= 6&& \text{multiply ALL terms by } \color{blue}{ (x+3)\cdot3 }. \\[1 em](x+3)\cdot3\cdot\frac{10}{x+3}+(x+3)\cdot3\cdot\frac{10}{3} &= (x+3)\cdot3\cdot6&& \text{cancel out the denominators} \\[1 em]30+10x+30 &= 18x+54&& \text{simplify left side} \\[1 em]10x+60 &= 18x+54&& \text{move the $ \color{blue}{ 18x } $ to the left side and $ \color{blue}{ 60 }$ to the right} \\[1 em]10x-18x &= 54-60&& \text{simplify left and right hand side} \\[1 em]-8x &= -6&& \text{ divide both sides by $ -8 $ } \\[1 em]x &= \frac{-6}{-8}&& \\[1 em]x &= \frac{3}{4}&& \\[1 em] \end{aligned} $$

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