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

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

Evaluate

$$x^{2}+x-7+\frac{3}{x}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{x^{3}+x^{2}-7x+3}{x}$$

Expand

$$x^{2}+x-7+\frac{3}{x}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{x^{3}+x^{2}-7x+3}{x}$$