Solve 1+2x+x^2/1+x^3div1+x/1-x+x^2

$$\frac { 1 + 2 x + x ^ { 2 } } { 1 + x ^ { 3 } } \div \frac { 1 + x } { 1 - x + x ^ { 2 } }$$

Evaluate

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Short Solution Steps

Divide \frac{1+2x+x^{2}}{1+x^{3}} by \frac{1+x}{1-x+x^{2}} by multiplying \frac{1+2x+x^{2}}{1+x^{3}} by the reciprocal of \frac{1+x}{1-x+x^{2}}.

$$\frac{\left(1+2x+x^{2}\right)\left(1-x+x^{2}\right)}{\left(1+x^{3}\right)\left(1+x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)^{2}\left(x^{2}-x+1\right)}{\left(x+1\right)^{2}\left(x^{2}-x+1\right)}$$

Cancel out \left(x+1\right)^{2}\left(x^{2}-x+1\right) in both numerator and denominator.

$$1$$

Factor

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