Solve 1/y^6-1/x^6=

$$\frac { 1 } { y ^ { 6 } } - \frac { 1 } { x ^ { 6 } } =$$

Evaluate

$$\frac{\left(x^{2}-y^{2}\right)\left(-\left(xy\right)^{2}+\left(x^{2}+y^{2}\right)^{2}\right)}{\left(xy\right)^{6}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{6} and x^{6} is x^{6}y^{6}. Multiply \frac{1}{y^{6}} times \frac{x^{6}}{x^{6}}. Multiply \frac{1}{x^{6}} times \frac{y^{6}}{y^{6}}.

$$\frac{x^{6}}{x^{6}y^{6}}-\frac{y^{6}}{x^{6}y^{6}}$$

Since \frac{x^{6}}{x^{6}y^{6}} and \frac{y^{6}}{x^{6}y^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{6}-y^{6}}{x^{6}y^{6}}$$

Factor

$$\frac{\frac{x^{6}}{y^{6}}-1}{x^{6}}$$