$$ \begin{aligned} \frac{x}{x+1}-\frac{x+1}{x} &= \frac{11}{30}&& \text{multiply ALL terms by } \color{blue}{ (x+1)x\cdot30 }. \\[1 em](x+1)x\cdot30 \cdot \frac{x}{x+1}-(x+1)x\cdot30\frac{x+1}{x} &= (x+1)x\cdot30\cdot\frac{11}{30}&& \text{cancel out the denominators} \\[1 em]30x^2-(30x^2+60x+30) &= 11x^2+11x&& \text{simplify left side} \\[1 em]30x^2-30x^2-60x-30 &= 11x^2+11x&& \\[1 em]30x^2-30x^2-60x-30 &= 11x^2+11x&& \\[1 em]-60x-30 &= 11x^2+11x&& \text{move all terms to the left hand side } \\[1 em]-60x-30-11x^2-11x &= 0&& \text{simplify left side} \\[1 em]-11x^2-71x-30 &= 0&& \\[1 em] \end{aligned} $$

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