Solve (x^4+1/x^4)(x-1/x)

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

Evaluate

$$\frac{\left(x^{2}-1\right)\left(x^{8}+1\right)}{x^{5}}$$

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}}.

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

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

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

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

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

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

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

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

$$\frac{x^{8}+1}{x^{4}}\times \frac{xx-1}{x}$$

Do the multiplications in xx-1.

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

Multiply \frac{x^{8}+1}{x^{4}} times \frac{x^{2}-1}{x} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\left(x^{8}+1\right)\left(x^{2}-1\right)}{x^{5}}$$

Use the distributive property to multiply x^{8}+1 by x^{2}-1.

$$\frac{x^{10}-x^{8}+x^{2}-1}{x^{5}}$$

Expand

$$x^{5}-x^{3}+\frac{1}{x^{3}}-\frac{1}{x^{5}}$$

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}}.

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

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

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

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

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

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

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

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

$$\frac{x^{8}+1}{x^{4}}\times \frac{xx-1}{x}$$

Do the multiplications in xx-1.

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

Multiply \frac{x^{8}+1}{x^{4}} times \frac{x^{2}-1}{x} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\left(x^{8}+1\right)\left(x^{2}-1\right)}{x^{5}}$$

Use the distributive property to multiply x^{8}+1 by x^{2}-1.

$$\frac{x^{10}-x^{8}+x^{2}-1}{x^{5}}$$