Solve x+1+2+x/x^2-4x+x

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

Evaluate

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

Short Solution Steps

Combine -4x and x to get -3x.

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

Factor x^{2}-3x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{x\left(x-3\right)}{x\left(x-3\right)}.

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

Since \frac{\left(x+1\right)x\left(x-3\right)}{x\left(x-3\right)} and \frac{2+x}{x\left(x-3\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x+1\right)x\left(x-3\right)+2+x.

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

Combine like terms in x^{3}-3x^{2}+x^{2}-3x+2+x.

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

Expand x\left(x-3\right).

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

Expand

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

Short Solution Steps

Combine -4x and x to get -3x.

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

Factor x^{2}-3x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{x\left(x-3\right)}{x\left(x-3\right)}.

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

Since \frac{\left(x+1\right)x\left(x-3\right)}{x\left(x-3\right)} and \frac{2+x}{x\left(x-3\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x+1\right)x\left(x-3\right)+2+x.

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

Combine like terms in x^{3}-3x^{2}+x^{2}-3x+2+x.

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

Expand x\left(x-3\right).

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