Solve 4k^2-4*left(4-x^2right)-4left(k^2-2right)/left(k^2-2right)*{k^{2}-left(4-2{k}^2right)left({k}^2+4kright)+left({k}^2+8k+16right){k}^2}

$$\frac{ 4 { k }^{ 2 } -4 \times \left( 4- { x }^{ 2 } \right) -4 \left( { k }^{ 2 } -2 \right) }{ \left( { k }^{ 2 } -2 \right) \times { k }^{ 2 } - \left( 4-2 { k }^{ 2 } \right) \left( { k }^{ 2 } +4k \right) + \left( { k }^{ 2 } +8k+16 \right) { k }^{ 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{2}-4}{2k^{4}+8k^{3}+5k^{2}-8k}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{2}-4}{2k^{4}+8k^{3}+5k^{2}-8k}$$