Question
$$\frac{1+2a}{1}+\frac{1}{1+2a} = 0$$
Answer
$$ \begin{matrix}a_1 = -\dfrac{ 1 }{ 2 }+\dfrac{ 1 }{ 2 }i & a_2 = -\dfrac{ 1 }{ 2 }-\dfrac{ 1 }{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+2a}{1}+\frac{1}{1+2a} &= 0&& \text{multiply ALL terms by } \color{blue}{ 1\cdot(1+2a) }. \\[1 em]1\cdot(1+2a)\frac{1+2a}{1}+1\cdot(1+2a)\cdot\frac{1}{1+2a} &= 1\cdot(1+2a)\cdot0&& \text{cancel out the denominators} \\[1 em]4a^2+4a+1+1 &= 0&& \text{simplify left side} \\[1 em]4a^2+4a+2 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+4x+2 = 0 $ is a quadratic equation.
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