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 Question from STEPHEN, a student: {(1+x)^1/3-1/3X(1+x)^-2/3}/(1+x)^2/3

Hi Stephen,

I would work with the numerator first,

$(1+x)^{1/3} -1/3 x (1+x)^{-2/3} = (1+x)^{1/3} - \frac{1/3 x}{(1+x)^{2/3}}.$

Express these two terms with the common denominator $(1+x)^{2/3}$ and simplify. Now reintroduce the original denominator by multiplying the simplified numerator by

$\frac{1}{(1+x)^{2/3}}.$

Penny

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