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

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

Evaluate

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

Short Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Factor

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