$$ \begin{aligned} \frac{5x+3}{x^2+11} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2+11 }. \\[1 em](x^2+11)\frac{5x+3}{x^2+11} &= (x^2+11)\cdot0&& \text{cancel out the denominators} \\[1 em]5x+3 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= -3&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{3}{5}&& \\[1 em] \end{aligned} $$

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