Question

How do you simplify `((1 - x^2)^(-1/3))(1 + x)^(1/3) - ((1 - x)^(2/3))(1 + x)^(-2/3)`?

Answer 1

I tried using one of the properties of the exponents but I didn't get such a huge simplification...actually, I think I complicated it! :-(

Explanation:

I used the fact that `x^(-b/a)=1/roota(x^b)` and get:
`1/root3((1-x)(1+x))*root3(1+x)-root3((1-x)^2)/(root3((1+x)^2))=`
`=root3(cancel((1+x))/(cancel((1+x))(1-x)))-root3((1-x)^2)/(root3((1+x)^2))=`
`=1/(root3(1-x))-root3((1-x)^2)/(root3((1+x)^2))=`
`=(root3((1+x)^2)-1+x)/(root3(1-x)*root3((1+x)^2)`