Solve 1/x^4-1/x^2

$$\frac { 1 } { x ^ { 4 } } - \frac { 1 } { x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{4} and x^{2} is x^{4}. Multiply \frac{1}{x^{2}} times \frac{x^{2}}{x^{2}}.

$$\frac{1}{x^{4}}-\frac{x^{2}}{x^{4}}$$

Since \frac{1}{x^{4}} and \frac{x^{2}}{x^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-x^{2}}{x^{4}}$$

Factor

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