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Question Number 99262 by Ar Brandon last updated on 19/Jun/20

$$\mathrm{Consider}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{xe}}^{\frac{1}{1-{\mathrm{x}}^2}}$$$$\mathrm{Find}3\mathrm{real}\mathrm{numbers}\mathrm{a},\mathrm{b},\mathrm{and}\mathrm{c}\mathrm{such}\mathrm{that}$$$$\mathrm{f}\left(\mathrm{x}\right)\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{in}\mathrm{the}\mathrm{form}\mathrm{ax}+\mathrm{b}+\frac{\mathrm{c}}{\mathrm{x}}+\frac{1}{\mathrm{x}}\xi \left(\mathrm{x}\right)$$$$\mathrm{where}\underset{\mathrm{x}\to \pm \mathrm{\infty }}{\lim }\xi \left(\mathrm{x}\right)=0$$

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