Solve (1/x-x)(x-1/x)=

$$( \frac{ 1 }{ x } -x)(x- \frac{ 1 }{ x } )=$$

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 1-xx.

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

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

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

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

$$\frac{1-x^{2}}{x}\times \frac{xx-1}{x}$$

Do the multiplications in xx-1.

$$\frac{1-x^{2}}{x}\times \frac{x^{2}-1}{x}$$

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

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

Multiply x and x to get x^{2}.

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

Apply the distributive property by multiplying each term of 1-x^{2} by each term of x^{2}-1.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in 1-xx.

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

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

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

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

$$\frac{1-x^{2}}{x}\times \frac{xx-1}{x}$$

Do the multiplications in xx-1.

$$\frac{1-x^{2}}{x}\times \frac{x^{2}-1}{x}$$

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

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

Multiply x and x to get x^{2}.

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

Apply the distributive property by multiplying each term of 1-x^{2} by each term of x^{2}-1.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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