How do you simplify (x+3)^(1/3) - (x+3)^(4/3) (x+3)13−(x+3)43?

1 Answer
Stefan V.
Oct 18, 2015

- (x+3)^(1/3) * (x + 2)−(x+3)13⋅(x+2)

Explanation:

You can simplify this expression by using (x+3)^(1/3)(x+3)13 as a commonfactor.

Focusing solely on the exponents, you need to find the relationship between 1/313, the exponent of the first term, and 4/343, the exponent of the second term, so that

1/3 + color(red)(x) = 4/3 implies color(red)(x) = 4/3 - 1/3 = 3/3 = 113+x=43⇒x=43−13=33=1

If you use (x+3)^(1/3)(x+3)13 as a common factor, you can thus write

(x+3)^(1/3) * [1 - (x+3)^(3/3)] = (x+3)^(1/3) * [1 - (x+3)^1](x+3)13⋅[1−(x+3)33]=(x+3)13⋅[1−(x+3)1]

=(x+3)^(1/3) * (1 - x - 3)=(x+3)13⋅(1−x−3)

= color(green)(- (x+3)^(1/3) * (x + 2))=−(x+3)13⋅(x+2)

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