Solve x^7-1/x^5

$$x ^ { 7 } - \frac { 1 } { x ^ { 5 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{7} times \frac{x^{5}}{x^{5}}.

$$\frac{x^{7}x^{5}}{x^{5}}-\frac{1}{x^{5}}$$

Since \frac{x^{7}x^{5}}{x^{5}} and \frac{1}{x^{5}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{7}x^{5}-1}{x^{5}}$$

Do the multiplications in x^{7}x^{5}-1.

$$\frac{x^{12}-1}{x^{5}}$$

Factor

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