$$ \begin{aligned} \frac{1}{x^2}+x^2 &= 4+\frac{1}{x}-x&& \text{multiply ALL terms by } \color{blue}{ x^2x }. \\[1 em]x^2x\cdot\frac{1}{x^2}+x^2xx^2 &= x^2x\cdot4+x^2x\cdot\frac{1}{x}-x^2xx&& \text{cancel out the denominators} \\[1 em]\frac{1}{x^1}+x^5 &= 4x^3+1-x^4&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot\frac{1}{x^1}+x^1\cdot1x^5 &= x^1\cdot4x^3+x^1\cdot1-x^1\cdot1x^4&& \text{cancel out the denominators} \\[1 em]1+x^6 &= 4x^4+x-x^5&& \text{simplify left and right hand side} \\[1 em]x^6+1 &= -x^5+4x^4+x&& \text{move all terms to the left hand side } \\[1 em]x^6+1+x^5-4x^4-x &= 0&& \text{simplify left side} \\[1 em]x^6+x^5-4x^4-x+1 &= 0&& \\[1 em] \end{aligned} $$

This page was created using