Question
$$\frac{x^2+5}{x+5}-\frac{x-16}{x+5} = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 83 }}{ 2 }i & x_2 = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 83 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x^2+5}{x+5}-\frac{x-16}{x+5} &= 0&& \text{multiply ALL terms by } \color{blue}{ x+5 }. \\[1 em](x+5)\frac{x^2+5}{x+5}-(x+5)\frac{x-16}{x+5} &= (x+5)\cdot0&& \text{cancel out the denominators} \\[1 em]x^2+5-(x-16) &= 0&& \text{simplify left side} \\[1 em]x^2+5-x+16 &= 0&& \\[1 em]x^2-x+21 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-x+21 = 0 $ is a quadratic equation.
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