Solve (x-1/x)divx+1/1

$$(x- \frac{ 1 }{ x } ) \div \frac{ x+1 }{ 1 }$$

Evaluate

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

Short Solution Steps

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

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

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

$$\frac{\frac{xx}{x}-\frac{1}{x}}{x+1}$$

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

$$\frac{\frac{xx-1}{x}}{x+1}$$

Do the multiplications in xx-1.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

$$\frac{\frac{xx}{x}-\frac{1}{x}}{x+1}$$

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

$$\frac{\frac{xx-1}{x}}{x+1}$$

Do the multiplications in xx-1.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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