Solve x(1-1/x^2)divx/2

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

Express x\times \frac{x^{2}-1}{x^{2}} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

Express x\times \frac{x^{2}-1}{x^{2}} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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