Know your limits! (IV)

Calculus Level 3

Evaluate limx1x1/2(2x)1/3x2+x2.\lim_{x\rightarrow1} \frac{x^{1/2}-(2-x)^{1/3}}{x^2+x-2} . If your answer can be expressed as ab\dfrac{a}{b} where aa and bb are coprime positive integers, find the value of a+ba+b.

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