$$ \begin{aligned} \frac{2x+2}{2x+3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2x+3 }. \\[1 em](2x+3)\frac{2x+2}{2x+3} &= (2x+3)\cdot0&& \text{cancel out the denominators} \\[1 em]2x+2 &= 0&& \text{ move the constants to the right } \\[1 em]2x &= -2&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{2}{2}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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