Solve -1+[x^2-4x+4divx-2]*(x+2)

$$- 1 + [ x ^ { 2 } - 4 x + 4 \div x - 2 ] \cdot ( x + 2 )$$

Evaluate

$$x^{3}-2x^{2}-10x-1+\frac{8}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-4x-2 times \frac{x}{x}.

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

Since \frac{\left(x^{2}-4x-2\right)x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{2}-4x-2\right)x+4.

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

Express \frac{x^{3}-4x^{2}-2x+4}{x}\left(x+2\right) as a single fraction.

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

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

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

Since -\frac{x}{x} and \frac{\left(x^{3}-4x^{2}-2x+4\right)\left(x+2\right)}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -x+\left(x^{3}-4x^{2}-2x+4\right)\left(x+2\right).

$$\frac{-x+x^{4}+2x^{3}-4x^{3}-8x^{2}-2x^{2}-4x+4x+8}{x}$$

Combine like terms in -x+x^{4}+2x^{3}-4x^{3}-8x^{2}-2x^{2}-4x+4x+8.

$$\frac{-x+x^{4}-2x^{3}-10x^{2}+8}{x}$$

Expand

$$x^{3}-2x^{2}-10x-1+\frac{8}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-4x-2 times \frac{x}{x}.

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

Since \frac{\left(x^{2}-4x-2\right)x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{2}-4x-2\right)x+4.

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

Express \frac{x^{3}-4x^{2}-2x+4}{x}\left(x+2\right) as a single fraction.

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

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

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

Since -\frac{x}{x} and \frac{\left(x^{3}-4x^{2}-2x+4\right)\left(x+2\right)}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -x+\left(x^{3}-4x^{2}-2x+4\right)\left(x+2\right).

$$\frac{-x+x^{4}+2x^{3}-4x^{3}-8x^{2}-2x^{2}-4x+4x+8}{x}$$

Combine like terms in -x+x^{4}+2x^{3}-4x^{3}-8x^{2}-2x^{2}-4x+4x+8.

$$\frac{-x+x^{4}-2x^{3}-10x^{2}+8}{x}$$