(2+x) to the negative 2/3power +(2+x)to the1/3 power(cube root) Can you help me factor?



Answers:
(2+x)^(-2/3) + (2+x)^(1/3)
You want to factor out the lowest power of (2+x).
Since -2/3 is less than 1/3, you will factor out (2+x)^(-2/3)

(2+x)^(-2/3) + (2+x)^(1/3)
= (2+x)^(-2/3) [1 + (2+x)^(1/3 +2/3)]
= (2+x)^(-2/3) [1 +(2+x)^1]
= (2+x)^(-2/3) (1+2+x)
= (2+x)^(-2/3) (x+3)
= (x+3) / (2+x)^(2/3)
Nope, sorry, I don't think I'm in that chapter yet
Sure, I'll help you! =)

In my explanation. ^ means "raised to the power of"

Given Problem: (2 + x)^(-2/3) + (2 + x)^(1/3)

** Hint: You want to factor out (2+x)^(1/3) from both terms **

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

**** Taking a look at the above, I factored out (2+x)^(1/3), but to figure out what goes INSIDE the [ ]'s, ask yourself...what "power" do you have to have that when added to 1/3 will give you the -2/3 that you have in the original problem? -3/3 , because 1/3 - 3/3 = -2/3 That's why you see me writing (-3/3) above. BUT. -3/3 is the equivalent of -1 ... so that's how come below, you see me writing -1 instead of -3/3 ****

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

Hope this helps!

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