$$\frac{5}{x-9}+\frac{2x+1}{x+5} = \frac{3x}{x+5}$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = 16 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{x-9}+\frac{2x+1}{x+5} &= \frac{3x}{x+5}&& \text{multiply ALL terms by } \color{blue}{ (x-9)(x+5) }. \\[1 em](x-9)(x+5)\cdot\frac{5}{x-9}+(x-9)(x+5)\frac{2x+1}{x+5} &= (x-9)(x+5)\frac{3x}{x+5}&& \text{cancel out the denominators} \\[1 em]5x+25+2x^2-17x-9 &= 3x^2-27x&& \text{simplify left side} \\[1 em]2x^2-12x+16 &= 3x^2-27x&& \text{move all terms to the left hand side } \\[1 em]2x^2-12x+16-3x^2+27x &= 0&& \text{simplify left side} \\[1 em]-x^2+15x+16 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+15x+16 = 0 $ is a quadratic equation.
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