Solve f(x)=x^6-x^2+x-1/x-x^3

$$f ( x ) = \frac { x ^ { 6 } - x ^ { 2 } + x - 1 } { x - x ^ { 3 } }$$

Evaluate

$$-\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{x\left(x+1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x^{5}+x^{4}+x^{3}+x^{2}+1\right)}{x\left(x-1\right)\left(-x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{x\left(-x-1\right)}$$

Expand the expression.

$$\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{-x^{2}-x}$$

Expand

$$-\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{x^{2}+x}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x^{5}+x^{4}+x^{3}+x^{2}+1\right)}{x\left(x-1\right)\left(-x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{x\left(-x-1\right)}$$

Expand the expression.

$$\frac{x^{5}+x^{4}+x^{3}+x^{2}+1}{-x^{2}-x}$$