Question
$$\frac{6}{x+1}+\frac{7}{x+5} = \frac{11}{x+1}(x+5)$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 97 }{ 22 }+\dfrac{\sqrt{ 1063 }}{ 22 }i & x_2 = -\dfrac{ 97 }{ 22 }-\dfrac{\sqrt{ 1063 }}{ 22 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{6}{x+1}+\frac{7}{x+5} &= \frac{11}{x+1}(x+5)&& \text{multiply ALL terms by } \color{blue}{ (x+1)(x+5) }. \\[1 em](x+1)(x+5)\cdot\frac{6}{x+1}+(x+1)(x+5)\cdot\frac{7}{x+5} &= (x+1)(x+5)\frac{11}{x+1}(x+5)&& \text{cancel out the denominators} \\[1 em]6x+30+7x+7 &= 11x^2+110x+275&& \text{simplify left side} \\[1 em]13x+37 &= 11x^2+110x+275&& \text{move all terms to the left hand side } \\[1 em]13x+37-11x^2-110x-275 &= 0&& \text{simplify left side} \\[1 em]-11x^2-97x-238 &= 0&& \\[1 em] \end{aligned} $$
$ -11x^{2}-97x-238 = 0 $ is a quadratic equation.
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