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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in x^{2}x^{2}+1.

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

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

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

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

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

Factor

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