Solve f(x)=(x+8)(x-5)/(x+2)(x+1)(x-2)

$$f ( x ) = \frac { ( x + 8 ) ( x - 5 ) } { ( x + 2 ) ( x + 1 ) ( x - 2 ) }$$

Evaluate

$$\frac{\left(x-5\right)\left(x+8\right)}{\left(x+1\right)\left(x^{2}-4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of x+8 by each term of x-5.

$$\frac{x^{2}-5x+8x-40}{\left(x+2\right)\left(x+1\right)\left(x-2\right)}$$

Combine -5x and 8x to get 3x.

$$\frac{x^{2}+3x-40}{\left(x+2\right)\left(x+1\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of x+2 by each term of x+1.

$$\frac{x^{2}+3x-40}{\left(x^{2}+x+2x+2\right)\left(x-2\right)}$$

Combine x and 2x to get 3x.

$$\frac{x^{2}+3x-40}{\left(x^{2}+3x+2\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of x^{2}+3x+2 by each term of x-2.

$$\frac{x^{2}+3x-40}{x^{3}-2x^{2}+3x^{2}-6x+2x-4}$$

Combine -2x^{2} and 3x^{2} to get x^{2}.

$$\frac{x^{2}+3x-40}{x^{3}+x^{2}-6x+2x-4}$$

Combine -6x and 2x to get -4x.

$$\frac{x^{2}+3x-40}{x^{3}+x^{2}-4x-4}$$

Expand

$$\frac{x^{2}+3x-40}{\left(x+1\right)\left(x^{2}-4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of x+8 by each term of x-5.

$$\frac{x^{2}-5x+8x-40}{\left(x+2\right)\left(x+1\right)\left(x-2\right)}$$

Combine -5x and 8x to get 3x.

$$\frac{x^{2}+3x-40}{\left(x+2\right)\left(x+1\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of x+2 by each term of x+1.

$$\frac{x^{2}+3x-40}{\left(x^{2}+x+2x+2\right)\left(x-2\right)}$$

Combine x and 2x to get 3x.

$$\frac{x^{2}+3x-40}{\left(x^{2}+3x+2\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of x^{2}+3x+2 by each term of x-2.

$$\frac{x^{2}+3x-40}{x^{3}-2x^{2}+3x^{2}-6x+2x-4}$$

Combine -2x^{2} and 3x^{2} to get x^{2}.

$$\frac{x^{2}+3x-40}{x^{3}+x^{2}-6x+2x-4}$$

Combine -6x and 2x to get -4x.

$$\frac{x^{2}+3x-40}{x^{3}+x^{2}-4x-4}$$