Solve (x^-4-x^2+x^-1):x^-1

$$( x ^ { - 4 } - x ^ { 2 } + x ^ { - 1 } ) : x ^ { - 1 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Expand the expression.

$$\frac{-x^{6}+x^{3}+1}{x^{3}}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Expand the expression.

$$\frac{-x^{6}+x^{3}+1}{x^{3}}$$