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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in 2xx-\left(1+x^{2}\right).

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

Combine like terms in 2x^{2}-1-x^{2}.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in 2xx-\left(1+x^{2}\right).

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

Combine like terms in 2x^{2}-1-x^{2}.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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