Solve 8x-32/x^{3+x^{2}}*x^5-x^4-2x^2/4x^2-16x+16

$$\frac { 8 x - 32 } { x ^ { 3 } + x ^ { 2 } } \cdot \frac { x ^ { 5 } - x ^ { 4 } - 2 x ^ { 2 } } { 4 x ^ { 2 } - 16 x + 16 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{8x-32}{x^{3}+x^{2}} times \frac{x^{5}-x^{4}-2x^{2}}{4x^{2}-16x+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x-32\right)\left(x^{5}-x^{4}-2x^{2}\right)}{\left(x^{3}+x^{2}\right)\left(4x^{2}-16x+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(x-4\right)x^{2}\left(x^{3}-x^{2}-2\right)}{4\left(x+1\right)x^{2}\left(x-2\right)^{2}}$$

Cancel out 4x^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{4}-10x^{3}+8x^{2}-4x+16}{x^{3}-3x^{2}+4}$$

Expand

$$\frac{2\left(x^{4}-5x^{3}+4x^{2}-2x+8\right)}{\left(x+1\right)\left(x^{2}-4x+4\right)}$$

Short Solution Steps

Multiply \frac{8x-32}{x^{3}+x^{2}} times \frac{x^{5}-x^{4}-2x^{2}}{4x^{2}-16x+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x-32\right)\left(x^{5}-x^{4}-2x^{2}\right)}{\left(x^{3}+x^{2}\right)\left(4x^{2}-16x+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(x-4\right)x^{2}\left(x^{3}-x^{2}-2\right)}{4\left(x+1\right)x^{2}\left(x-2\right)^{2}}$$

Cancel out 4x^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{4}-10x^{3}+8x^{2}-4x+16}{x^{3}-3x^{2}+4}$$