$$ \begin{aligned} x+\frac{3}{x}+5 &= x-\frac{2}{x}+3&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx+x\cdot\frac{3}{x}+x\cdot5 &= xx-x\cdot\frac{2}{x}+x\cdot3&& \text{cancel out the denominators} \\[1 em]x^2+3+5x &= x^2-2+3x&& \text{simplify left and right hand side} \\[1 em]x^2+5x+3 &= x^2+3x-2&& \text{move all terms to the left hand side } \\[1 em]x^2+5x+3-x^2-3x+2 &= 0&& \text{simplify left side} \\[1 em]x^2+5x+3-x^2-3x+2 &= 0&& \\[1 em]2x+5 &= 0&& \text{ move the constants to the right } \\[1 em]2x &= -5&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{5}{2}&& \\[1 em] \end{aligned} $$
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