Solve 16/left(x^2-2right)^2-2

$$\frac{ 16 }{ { \left( { x }^{ 2 } -2 \right) }^{ 2 } } -2$$

Evaluate

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

Short Solution Steps

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

$$\frac{16}{\left(x^{2}-2\right)^{2}}-\frac{2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}}$$

Since \frac{16}{\left(x^{2}-2\right)^{2}} and \frac{2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}}$$

Do the multiplications in 16-2\left(x^{2}-2\right)^{2}.

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

Combine like terms in 16-2x^{4}+8x^{2}-8.

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

Expand \left(x^{2}-2\right)^{2}.

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

Expand

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

Short Solution Steps

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

$$\frac{16}{\left(x^{2}-2\right)^{2}}-\frac{2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}}$$

Since \frac{16}{\left(x^{2}-2\right)^{2}} and \frac{2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-2\left(x^{2}-2\right)^{2}}{\left(x^{2}-2\right)^{2}}$$

Do the multiplications in 16-2\left(x^{2}-2\right)^{2}.

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

Combine like terms in 16-2x^{4}+8x^{2}-8.

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

Expand \left(x^{2}-2\right)^{2}.

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