Question 150980

{{{(x^4-3x)/(3x-x^4)}}} Start with the given expression.



{{{(x*(x^3-3))/(3x-x^4)}}} Factor {{{x^4-3x}}} to get {{{x*(x^3-3)}}}.



{{{(x*(x^3-3))/(-x*(x^3-3))}}} Factor {{{3x-x^4}}} to get {{{-x*(x^3-3)}}}.



{{{-(highlight(x)highlight((x^3-3)))/(highlight(x)highlight((x^3-3)))}}} Highlight the common terms. 



{{{-(cross(x)cross((x^3-3)))/(cross(x)cross((x^3-3)))}}} Cancel out the common terms. 



{{{-1}}} Simplify. 



So {{{(x^4-3x)/(3x-x^4)}}} simplifies to {{{-1}}}.



In other words, {{{(x^4-3x)/(3x-x^4)=-1}}} where {{{x<>0}}} or {{{x<>root(3,3)}}}