Question

Simplify and show work:

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


My answer key says that it's this but I have no idea how to get to it. I've tried 4 times already:

[-(x^(2)+9)]/[(3x^(2))(x^(2)+3))^(2/3)]

Answer 1

you cannot simplify with negatives

[(X^(2)+3)^(1/3)](-1)(x^(-2))+[1/3(x^(2)+3)^(-2/3)](2x)(x^(-1))
so the real question is
[(X^2)+3)^(1/3)](-1)(x^(-2))+[1/3(x^(2)+3)^(-2/3)](2x)(x^(-1))
i hope this helped

Answer 2

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

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

I entered it exactly the way you typed it, and did not get that answer.
Check your brackets

http://www.wolframalpha.com/input/?i=simplify+%5B(X%5E(2)%2B3)%5E(1%2F3)%5D(-1)(x%5E(-2))%2B%5B1%2F3(x%5E(2)%2B3)%5E(-2%2F3)%5D(2x)(x%5E(-1))

Answer 3

Go to Reiny's url and tweak the input until it agrees with what you intended. It's probably just a combination of typos.