Question
$$\frac{1}{a}-\frac{1}{2a} = \frac{1}{2a}$$
Answer
$$ \begin{matrix}a_1 = 1 & a_2 = -1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{a}-\frac{1}{2a} &= \frac{1}{2a}&& \text{multiply ALL terms by } \color{blue}{ a\cdot2 }. \\[1 em]a\cdot2\cdot\frac{1}{a}-a\cdot2\cdot\frac{1}{2a} &= a\cdot2\cdot\frac{1}{2a}&& \text{cancel out the denominators} \\[1 em]2-a^2 &= a^2&& \text{simplify left side} \\[1 em]-a^2+2 &= a^2&& \text{move all terms to the left hand side } \\[1 em]-a^2+2-a^2 &= 0&& \text{simplify left side} \\[1 em]-2a^2+2 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}+2 = 0 $ is a quadratic equation.
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