Simplifying algebra

Question

I am not sure how ti simplify this expression

 

2(x-2)²(2x+1)^-1/3 - (x-2)(2x+1)^2/3

 

The furthest I can get is 

 

2(x-2)2/(2x+1)^1/3 - (x-2)(2x+1)^2/3

 

I have brought the power down to make it positive but not sure if this is the question simplified or is there more to simplify it further. Any detailed explanation would be great

 

Answer 1

You are on the right path, for sure. What else can you do to add or subtract two fractions? Find a common denominator.

 

If you multiply the right group by (2x+1)^1/3/(2x+1)^1/3 it can simplify a little bit more.

 

You end up with

 

(x-2) [2 (x-2) - (2x+1) ]

      (2x+1)^1/3

 

The numerator can simplify if you expand further. This results in

 

-5x + 10 

(2x+1)^1/3

 

I wish you the best of luck on this problem!

 

Edit: Those rows of polynomials are supposed to be underlined, indicating they they are fractions.