$$ \begin{aligned} -4 &= \frac{y+3}{y+10}&& \text{multiply ALL terms by } \color{blue}{ y+10 }. \\[1 em](y+10)\cdot(-4) &= (y+10)\frac{y+3}{y+10}&& \text{cancel out the denominators} \\[1 em]-4y-40 &= y+3&& \text{move the $ \color{blue}{ y } $ to the left side and $ \color{blue}{ -40 }$ to the right} \\[1 em]-4y-y &= 3+40&& \text{simplify left and right hand side} \\[1 em]-5y &= 43&& \text{ divide both sides by $ -5 $ } \\[1 em]y &= -\frac{43}{5}&& \\[1 em] \end{aligned} $$

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