$$\frac{p+10}{p^2-2} = \frac{4}{p}$$
Answer
$$ \begin{matrix}p_1 = -\dfrac{ 2 }{ 3 } & p_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{p+10}{p^2-2} &= \frac{4}{p}&& \text{multiply ALL terms by } \color{blue}{ (p^2-2)p }. \\[1 em](p^2-2)p\frac{p+10}{p^2-2} &= (p^2-2)p\cdot\frac{4}{p}&& \text{cancel out the denominators} \\[1 em]p^2+10p &= 4p^2-8&& \text{move all terms to the left hand side } \\[1 em]p^2+10p-4p^2+8 &= 0&& \text{simplify left side} \\[1 em]-3p^2+10p+8 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+10x+8 = 0 $ is a quadratic equation.
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