Solve (x^4+1/x^4)div(x^2+1/x^2)

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

Evaluate

$$\frac{x^{8}+1}{x^{2}\left(x^{4}+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{x^{4}}{x^{4}}.

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

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

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

Do the multiplications in x^{4}x^{4}+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Divide \frac{x^{8}+1}{x^{4}} by \frac{x^{4}+1}{x^{2}} by multiplying \frac{x^{8}+1}{x^{4}} by the reciprocal of \frac{x^{4}+1}{x^{2}}.

$$\frac{\left(x^{8}+1\right)x^{2}}{x^{4}\left(x^{4}+1\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{8}+1}{x^{2}\left(x^{4}+1\right)}$$

Use the distributive property to multiply x^{2} by x^{4}+1.

$$\frac{x^{8}+1}{x^{6}+x^{2}}$$

Expand

$$\frac{x^{8}+1}{x^{2}\left(x^{4}+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{x^{4}}{x^{4}}.

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

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

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

Do the multiplications in x^{4}x^{4}+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Divide \frac{x^{8}+1}{x^{4}} by \frac{x^{4}+1}{x^{2}} by multiplying \frac{x^{8}+1}{x^{4}} by the reciprocal of \frac{x^{4}+1}{x^{2}}.

$$\frac{\left(x^{8}+1\right)x^{2}}{x^{4}\left(x^{4}+1\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{8}+1}{x^{2}\left(x^{4}+1\right)}$$

Use the distributive property to multiply x^{2} by x^{4}+1.

$$\frac{x^{8}+1}{x^{6}+x^{2}}$$