$$\frac{5}{x+3}+3\frac{x}{x+4} = 2$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = -2 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{x+3}+3\frac{x}{x+4} &= 2&& \text{multiply ALL terms by } \color{blue}{ (x+3)(x+4) }. \\[1 em](x+3)(x+4)\cdot\frac{5}{x+3}+(x+3)(x+4)\cdot3\frac{x}{x+4} &= (x+3)(x+4)\cdot2&& \text{cancel out the denominators} \\[1 em]5x+20+3x^2+9x &= 2x^2+14x+24&& \text{simplify left side} \\[1 em]3x^2+14x+20 &= 2x^2+14x+24&& \text{move all terms to the left hand side } \\[1 em]3x^2+14x+20-2x^2-14x-24 &= 0&& \text{simplify left side} \\[1 em]3x^2+14x+20-2x^2-14x-24 &= 0&& \\[1 em]x^2-4 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-4 = 0 $ is a quadratic equation.
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