Solve -10x^2-24x-48/left(x+2right)left(x-3right)left(x^2+x+2right)

$$\frac{ -10 { x }^{ 2 } -24x-48 }{ \left( x+2 \right) \left( x-3 \right) \left( { x }^{ 2 } +x+2 \right) }$$

Evaluate

$$-\frac{2\left(5x^{2}+12x+24\right)}{\left(x-3\right)\left(x+2\right)\left(x^{2}+x+2\right)}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$\frac{-10x^{2}-24x-48}{\left(x^{2}-x-6\right)\left(x^{2}+x+2\right)}$$

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

$$\frac{-10x^{2}-24x-48}{x^{4}-5x^{2}-8x-12}$$

Expand

$$-\frac{2\left(5x^{2}+12x+24\right)}{\left(x-3\right)\left(x+2\right)\left(x^{2}+x+2\right)}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$\frac{-10x^{2}-24x-48}{\left(x^{2}-x-6\right)\left(x^{2}+x+2\right)}$$

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

$$\frac{-10x^{2}-24x-48}{x^{4}-5x^{2}-8x-12}$$