Solve 2-2x^2/1+2x^2+x^4*1/2x^2

$$\frac{ 2-2 { x }^{ 2 } }{ 1+2 { x }^{ 2 } + { x }^{ 4 } } \times \frac{ 1 }{ 2 { x }^{ 2 } }$$

Evaluate

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

Short Solution Steps

Multiply \frac{2-2x^{2}}{1+2x^{2}+x^{4}} times \frac{1}{2x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{-x^{2}+1}{x^{6}+2x^{4}+x^{2}}$$

Expand

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

Short Solution Steps

Multiply \frac{2-2x^{2}}{1+2x^{2}+x^{4}} times \frac{1}{2x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{-x^{2}+1}{x^{6}+2x^{4}+x^{2}}$$