Solve (x-1)*(x^3+x^2-2x-2+(3div(x-1)))

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

Evaluate

$$x^{4}-3x^{2}+5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+x^{2}-2x-2 times \frac{x-1}{x-1}.

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

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

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

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

$$\left(x-1\right)\times \frac{x^{4}-x^{3}+x^{3}-x^{2}-2x^{2}+2x-2x+2+3}{x-1}$$

Combine like terms in x^{4}-x^{3}+x^{3}-x^{2}-2x^{2}+2x-2x+2+3.

$$\left(x-1\right)\times \frac{x^{4}-3x^{2}+5}{x-1}$$

Cancel out x-1 and x-1.

$$x^{4}-3x^{2}+5$$

Expand

$$x^{4}-3x^{2}+5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+x^{2}-2x-2 times \frac{x-1}{x-1}.

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

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

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

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

$$\left(x-1\right)\times \frac{x^{4}-x^{3}+x^{3}-x^{2}-2x^{2}+2x-2x+2+3}{x-1}$$

Combine like terms in x^{4}-x^{3}+x^{3}-x^{2}-2x^{2}+2x-2x+2+3.

$$\left(x-1\right)\times \frac{x^{4}-3x^{2}+5}{x-1}$$

Cancel out x-1 and x-1.

$$x^{4}-3x^{2}+5$$