Calculus help. Finding the inverse.

How do I find the inverse equation of y = (1 - x^(1/3))/(1 + x^(1/3)) ?

I know the steps for finding the inverse are to solve the equation for x and then switch the x for y and y for x, but for the life of me I can not solve for x. What do I do? Do I take the natural log of both sides or do I multiply out by the conjugate?

Since the numerator and denominator are the same degree, you could try long division to rewrite:

[-x^(1/3)+1] -:- [x^(1/3)+1]= -1 + 2/[x^(1/3)+1]

Then switch variables:

X= -1+ 2/[y^(1/3)+1]

(x+1)= 2/[y^(1/3)+1]

Y^(1/3)+1= 2/(x+1)

Y= [2/(x+1)-1]^3

=[ (1-x)/(x-1)]^3

Hoping this helps!

That last denominator should be x +1. Thanks for double checking!
Good luck!

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y + x^(1/3) (1 + y) == 1

x^(1/3)+1!=0, y = (1-x^(1/3))/(x^(1/3)+1)