Simplify - 1 - 2 x - x 2 1 - x 3 - 1 - x - x 2 1 - x

[ 1 2x+ x^ 2 1 x^ 3 × 1+x+ x^ 2 1+x ...

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Division of a Polynomial by a Polynomial

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Question

Simplify : $\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}$

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\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}

\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}

(1 + x + x^{2}) (1 - \frac{x}{1!} + \frac{x^{2}}{2!} - \frac{x^{3}}{3!} + \dots) = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + a_{4} x^{4} + . . .

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