Solve (x^2+x/1-(x+1)divx^3+x^2/x^2-2x+1)

$$( \frac { x ^ { 2 } + x } { 1 } - ( x + 1 ) \div \frac { x ^ { 3 } + x ^ { 2 } } { x ^ { 2 } - 2 x + 1 } )$$

Evaluate

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

Short Solution Steps

Anything divided by one gives itself.

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

Divide x+1 by \frac{x^{3}+x^{2}}{x^{2}-2x+1} by multiplying x+1 by the reciprocal of \frac{x^{3}+x^{2}}{x^{2}-2x+1}.

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

Factor the expressions that are not already factored in \frac{\left(x+1\right)\left(x^{2}-2x+1\right)}{x^{3}+x^{2}}.

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

Cancel out x+1 in both numerator and denominator.

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

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

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

Since \frac{\left(x^{2}+x\right)x^{2}}{x^{2}} and \frac{\left(x-1\right)^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{x^{4}+x^{3}-x^{2}+2x-1}{x^{2}}$$

Expand

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

Short Solution Steps

Anything divided by one gives itself.

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

Divide x+1 by \frac{x^{3}+x^{2}}{x^{2}-2x+1} by multiplying x+1 by the reciprocal of \frac{x^{3}+x^{2}}{x^{2}-2x+1}.

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

Factor the expressions that are not already factored in \frac{\left(x+1\right)\left(x^{2}-2x+1\right)}{x^{3}+x^{2}}.

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

Cancel out x+1 in both numerator and denominator.

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

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

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

Since \frac{\left(x^{2}+x\right)x^{2}}{x^{2}} and \frac{\left(x-1\right)^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{x^{4}+x^{3}-x^{2}+2x-1}{x^{2}}$$