Solve (x^2+1/x)(x-1/x^3)

$$( { x }^{ 2 } + \frac{ 1 }{ x } )(x- \frac{ 1 }{ { x }^{ 3 } } )$$

Evaluate

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

Short Solution Steps

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

$$\left(\frac{x^{2}x}{x}+\frac{1}{x}\right)\left(x-\frac{1}{x^{3}}\right)$$

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

$$\frac{x^{2}x+1}{x}\left(x-\frac{1}{x^{3}}\right)$$

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

$$\frac{x^{3}+1}{x}\left(x-\frac{1}{x^{3}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x^{3}}{x^{3}}.

$$\frac{x^{3}+1}{x}\left(\frac{xx^{3}}{x^{3}}-\frac{1}{x^{3}}\right)$$

Since \frac{xx^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{3}+1}{x}\times \frac{xx^{3}-1}{x^{3}}$$

Do the multiplications in xx^{3}-1.

$$\frac{x^{3}+1}{x}\times \frac{x^{4}-1}{x^{3}}$$

Multiply \frac{x^{3}+1}{x} times \frac{x^{4}-1}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{3}+1\right)\left(x^{4}-1\right)}{xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\left(x^{3}+1\right)\left(x^{4}-1\right)}{x^{4}}$$

Use the distributive property to multiply x^{3}+1 by x^{4}-1.

$$\frac{x^{7}-x^{3}+x^{4}-1}{x^{4}}$$

Expand

$$x^{3}+1-\frac{1}{x}-\frac{1}{x^{4}}$$

Short Solution Steps

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

$$\left(\frac{x^{2}x}{x}+\frac{1}{x}\right)\left(x-\frac{1}{x^{3}}\right)$$

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

$$\frac{x^{2}x+1}{x}\left(x-\frac{1}{x^{3}}\right)$$

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

$$\frac{x^{3}+1}{x}\left(x-\frac{1}{x^{3}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x^{3}}{x^{3}}.

$$\frac{x^{3}+1}{x}\left(\frac{xx^{3}}{x^{3}}-\frac{1}{x^{3}}\right)$$

Since \frac{xx^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{3}+1}{x}\times \frac{xx^{3}-1}{x^{3}}$$

Do the multiplications in xx^{3}-1.

$$\frac{x^{3}+1}{x}\times \frac{x^{4}-1}{x^{3}}$$

Multiply \frac{x^{3}+1}{x} times \frac{x^{4}-1}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{3}+1\right)\left(x^{4}-1\right)}{xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\left(x^{3}+1\right)\left(x^{4}-1\right)}{x^{4}}$$

Use the distributive property to multiply x^{3}+1 by x^{4}-1.

$$\frac{x^{7}-x^{3}+x^{4}-1}{x^{4}}$$