Solve (x^{2}*frac{x^{3}-1}{x^2+x+1}):x^3-x^2+x/x^3+1

$$( x ^ { 2 } \cdot \frac { x ^ { 3 } - 1 } { x ^ { 2 } + x + 1 } ) : \frac { x ^ { 3 } - x ^ { 2 } + x } { x ^ { 3 } + 1 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}-1}{x^{2}+x+1}.

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

Cancel out x^{2}+x+1 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{3}-x^{2}+x}{x^{3}+1}.

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

Cancel out x^{2}-x+1 in both numerator and denominator.

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

Divide x^{2}\left(x-1\right) by \frac{x}{x+1} by multiplying x^{2}\left(x-1\right) by the reciprocal of \frac{x}{x+1}.

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

Cancel out x in both numerator and denominator.

$$x\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply x by x-1.

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

Use the distributive property to multiply x^{2}-x by x+1 and combine like terms.

$$x^{3}-x$$

Expand

$$x^{3}-x$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}-1}{x^{2}+x+1}.

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

Cancel out x^{2}+x+1 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{3}-x^{2}+x}{x^{3}+1}.

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

Cancel out x^{2}-x+1 in both numerator and denominator.

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

Divide x^{2}\left(x-1\right) by \frac{x}{x+1} by multiplying x^{2}\left(x-1\right) by the reciprocal of \frac{x}{x+1}.

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

Cancel out x in both numerator and denominator.

$$x\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply x by x-1.

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

Use the distributive property to multiply x^{2}-x by x+1 and combine like terms.

$$x^{3}-x$$