Solve 1/x^2-1/8*1/y^6

$$\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 8 } \cdot \frac { 1 } { y ^ { 6 } }$$

Evaluate

$$\frac{1}{x^{2}}-\frac{1}{8y^{6}}$$

Solution Steps

Multiply \frac{1}{8} times \frac{1}{y^{6}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{x^{2}}-\frac{1}{8y^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and 8y^{6} is 8x^{2}y^{6}. Multiply \frac{1}{x^{2}} times \frac{8y^{6}}{8y^{6}}. Multiply \frac{1}{8y^{6}} times \frac{x^{2}}{x^{2}}.

$$\frac{8y^{6}}{8x^{2}y^{6}}-\frac{x^{2}}{8x^{2}y^{6}}$$

Since \frac{8y^{6}}{8x^{2}y^{6}} and \frac{x^{2}}{8x^{2}y^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8y^{6}-x^{2}}{8x^{2}y^{6}}$$

Factor

$$\frac{8-\frac{x^{2}}{y^{6}}}{8x^{2}}$$