$$\frac{x+10}{2}-\frac{13}{x+1} = \frac{11}{3}$$
Answer
$$ \begin{matrix}x_1 = -7 & x_2 = \dfrac{ 10 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x+10}{2}-\frac{13}{x+1} &= \frac{11}{3}&& \text{multiply ALL terms by } \color{blue}{ 2(x+1)\cdot3 }. \\[1 em]2(x+1)\cdot3 \cdot \frac{x+10}{2}-2(x+1)\cdot3\cdot\frac{13}{x+1} &= 2(x+1)\cdot3\cdot\frac{11}{3}&& \text{cancel out the denominators} \\[1 em]3x^2+33x+30-78 &= 22x+22&& \text{simplify left side} \\[1 em]3x^2+33x-48 &= 22x+22&& \text{move all terms to the left hand side } \\[1 em]3x^2+33x-48-22x-22 &= 0&& \text{simplify left side} \\[1 em]3x^2+11x-70 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+11x-70 = 0 $ is a quadratic equation.
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