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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in \left(x^{4}+2\right)x^{4}+1.

$$\frac{x^{8}+2x^{4}+1}{4x^{4}}$$

Factor

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