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

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

Evaluate

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Short Solution Steps

Subtract 2 from 4 to get 2.

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

Subtract 4 from 2 to get -2.

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

Factor 1+x^{-2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1+x^{2} and x^{-2}\left(x^{2}+1\right) is x^{-2}\left(x^{2}+1\right). Multiply \frac{1}{1+x^{2}} times \frac{x^{-2}}{x^{-2}}.

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

Since \frac{x^{-2}}{x^{-2}\left(x^{2}+1\right)} and \frac{1}{x^{-2}\left(x^{2}+1\right)} have the same denominator, add them by adding their numerators.

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

Factor the expressions that are not already factored in \frac{x^{-2}+1}{x^{-2}\left(x^{2}+1\right)}.

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

Cancel out x^{-2}\left(x^{2}+1\right) in both numerator and denominator.

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Factor

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