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Can this be simplified.?
I'm looking at this problem.
(x-27)/(x^1/3 - 3)
And for the life of me I can't remember if this can be simplified. Can I call x^1/3-3 x-27 times two other factors somehow?
4 Answers
- jimbotLv 61 decade agoFavorite Answer
let u = x^(1/3)
the equation becomes
(u³ - 27)/(u - 3)
the numerator is a difference of cubes, so factor and cancel:
(u - 3)(u² + 3u + 9) / (u - 3)
= u² + 3u + 9
subbing x back in:
= x^(2/3) + 3x^(1/3) + 9
- ThinkerLv 41 decade ago
Yes, it can be simplified.
Recall: (x^1/3)^3 = x Then in numerator:
[(x^1/3)^3 - 3^3]/[(x^1/3) - 3] =
(x^1/3 - 3)[(x^1/3)^2 + 3(x^1/3) + 9]/(x^1/3 - 3) =
(x^1/3)^2 + 3(x^1/3) + 9
- 1 decade ago
no they cannot. Since they are both subtracting you can not simplify them
Source(s): AP calculus
