Question
$$3 = \frac{9x^2}{x^2+1}-2$$
Answer
$$ \begin{matrix}x_1 = - \dfrac{\sqrt{ 5 }}{ 2 } & x_2 = \dfrac{\sqrt{ 5 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3 &= \frac{9x^2}{x^2+1}-2&& \text{multiply ALL terms by } \color{blue}{ x^2+1 }. \\[1 em](x^2+1)\cdot3 &= (x^2+1)\frac{9x^2}{x^2+1}-(x^2+1)\cdot2&& \text{cancel out the denominators} \\[1 em]3x^2+3 &= 9x^2-(2x^2+2)&& \text{simplify right side} \\[1 em]3x^2+3 &= 9x^2-2x^2-2&& \\[1 em]3x^2+3 &= 7x^2-2&& \text{move all terms to the left hand side } \\[1 em]3x^2+3-7x^2+2 &= 0&& \text{simplify left side} \\[1 em]-4x^2+5 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+5 = 0 $ is a quadratic equation.
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