Simplifying expressions on Mathematica is a recurrent topic. However I found myself stuck with this one:
Solving an rational equation on Mathematica gives me the following expression:
expression := -((2 x)/3) + (2^(1/3) (3 - x^2))/(
3 (9 x - 2 x^3 + Sqrt[4 (3 - x^2)^3 + (9 x - 2 x^3)^2])^(
1/3)) - (9 x - 2 x^3 + Sqrt[4 (3 - x^2)^3 + (9 x - 2 x^3)^2])^(
1/3)/(3 2^(1/3))
I know that the expression should simply to $-x$. If I plot the expression I get indeed a plot of $y=-x$.
Plot[expression, {x, -1, 1}]
I tried using the function "Simplify", "FullSimplify" even "Expand" and then "Simplify" but got no luck as I do not have restriction on $x$. The expression is very messy and I do not manage to simplify it by hand. How could I use mathematica to simplify "expression" to $-x$? (other than using a graphical plot)
Any idea are much appreciated! Thanks
Plot[expression, {x, -10, 2}]
? $\endgroup$In[348]:= First[GroebnerBasis[expression, x]] Out[348]= x
$\endgroup$