$$ \begin{aligned} 2x+\frac{5}{x}+4 &= x+\frac{2}{x}+4&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2x+x\cdot\frac{5}{x}+x\cdot4 &= xx+x\cdot\frac{2}{x}+x\cdot4&& \text{cancel out the denominators} \\[1 em]2x^2+5+4x &= x^2+2+4x&& \text{simplify left and right hand side} \\[1 em]2x^2+4x+5 &= x^2+4x+2&& \text{move all terms to the left hand side } \\[1 em]2x^2+4x+5-x^2-4x-2 &= 0&& \text{simplify left side} \\[1 em]2x^2+4x+5-x^2-4x-2 &= 0&& \\[1 em]x^2+3 &= 0&& \\[1 em] \end{aligned} $$

This page was created using