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

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

Evaluate

$$2$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x^{2}-1\right)\left(x+1\right)}{x^{2}-x}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

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

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

Divide \frac{\left(x+1\right)^{2}}{x} by \frac{2x+x^{2}+1}{2x} by multiplying \frac{\left(x+1\right)^{2}}{x} by the reciprocal of \frac{2x+x^{2}+1}{2x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x+1\right)^{2} in both numerator and denominator.

$$2$$

Factor

$$2$$