Solve 1-x^2/x-frac{1{x}}-2/x^3

$$\frac{ 1- { x }^{ 2 } }{ x- \frac{ 1 }{ x } } - \frac{ 2 }{ { x }^{ 3 } }$$

Evaluate

$$-x-\frac{2}{x^{3}}$$

Short Solution Steps

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

$$\frac{1-x^{2}}{\frac{xx}{x}-\frac{1}{x}}-\frac{2}{x^{3}}$$

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

$$\frac{1-x^{2}}{\frac{xx-1}{x}}-\frac{2}{x^{3}}$$

Do the multiplications in xx-1.

$$\frac{1-x^{2}}{\frac{x^{2}-1}{x}}-\frac{2}{x^{3}}$$

Divide 1-x^{2} by \frac{x^{2}-1}{x} by multiplying 1-x^{2} by the reciprocal of \frac{x^{2}-1}{x}.

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

Extract the negative sign in 1-x^{2}.

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

Cancel out x^{2}-1 in both numerator and denominator.

$$-x-\frac{2}{x^{3}}$$

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

$$-\frac{xx^{3}}{x^{3}}-\frac{2}{x^{3}}$$

Since -\frac{xx^{3}}{x^{3}} and \frac{2}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-xx^{3}-2}{x^{3}}$$

Do the multiplications in -xx^{3}-2.

$$\frac{-x^{4}-2}{x^{3}}$$

Expand

$$-x-\frac{2}{x^{3}}$$

Short Solution Steps

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

$$\frac{1-x^{2}}{\frac{xx}{x}-\frac{1}{x}}-\frac{2}{x^{3}}$$

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

$$\frac{1-x^{2}}{\frac{xx-1}{x}}-\frac{2}{x^{3}}$$

Do the multiplications in xx-1.

$$\frac{1-x^{2}}{\frac{x^{2}-1}{x}}-\frac{2}{x^{3}}$$

Divide 1-x^{2} by \frac{x^{2}-1}{x} by multiplying 1-x^{2} by the reciprocal of \frac{x^{2}-1}{x}.

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

Extract the negative sign in 1-x^{2}.

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

Cancel out x^{2}-1 in both numerator and denominator.

$$-x-\frac{2}{x^{3}}$$

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

$$-\frac{xx^{3}}{x^{3}}-\frac{2}{x^{3}}$$

Since -\frac{xx^{3}}{x^{3}} and \frac{2}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-xx^{3}-2}{x^{3}}$$

Do the multiplications in -xx^{3}-2.

$$\frac{-x^{4}-2}{x^{3}}$$