Solve 4-((x+3)x^2+5x-6/x-2)

$$4-((x+3) \frac{ { x }^{ 2 } +5x-6 }{ x-2 } )$$

Evaluate

$$\frac{10-5x-8x^{2}-x^{3}}{x-2}$$

Short Solution Steps

Express \left(x+3\right)\times \frac{x^{2}+5x-6}{x-2} as a single fraction.

$$4-\frac{\left(x+3\right)\left(x^{2}+5x-6\right)}{x-2}$$

Use the distributive property to multiply x+3 by x^{2}+5x-6 and combine like terms.

$$4-\frac{x^{3}+8x^{2}+9x-18}{x-2}$$

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

$$\frac{4\left(x-2\right)}{x-2}-\frac{x^{3}+8x^{2}+9x-18}{x-2}$$

Since \frac{4\left(x-2\right)}{x-2} and \frac{x^{3}+8x^{2}+9x-18}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x-2\right)-\left(x^{3}+8x^{2}+9x-18\right)}{x-2}$$

Do the multiplications in 4\left(x-2\right)-\left(x^{3}+8x^{2}+9x-18\right).

$$\frac{4x-8-x^{3}-8x^{2}-9x+18}{x-2}$$

Combine like terms in 4x-8-x^{3}-8x^{2}-9x+18.

$$\frac{-5x+10-x^{3}-8x^{2}}{x-2}$$

Expand

$$\frac{10-5x-8x^{2}-x^{3}}{x-2}$$

Short Solution Steps

Express \left(x+3\right)\times \frac{x^{2}+5x-6}{x-2} as a single fraction.

$$4-\frac{\left(x+3\right)\left(x^{2}+5x-6\right)}{x-2}$$

Use the distributive property to multiply x+3 by x^{2}+5x-6 and combine like terms.

$$4-\frac{x^{3}+8x^{2}+9x-18}{x-2}$$

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

$$\frac{4\left(x-2\right)}{x-2}-\frac{x^{3}+8x^{2}+9x-18}{x-2}$$

Since \frac{4\left(x-2\right)}{x-2} and \frac{x^{3}+8x^{2}+9x-18}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x-2\right)-\left(x^{3}+8x^{2}+9x-18\right)}{x-2}$$

Do the multiplications in 4\left(x-2\right)-\left(x^{3}+8x^{2}+9x-18\right).

$$\frac{4x-8-x^{3}-8x^{2}-9x+18}{x-2}$$

Combine like terms in 4x-8-x^{3}-8x^{2}-9x+18.

$$\frac{-5x+10-x^{3}-8x^{2}}{x-2}$$