Simplify (x^4-2)/(x^2-2)+2/(-x^2+2)

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

Simplify terms.

Factor $- 1$ out of $- x^{2}$ .

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

Rewrite $2$ as $- 1 (- 2)$ .

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

Factor $- 1$ out of $- (x^{2}) - 1 (- 2)$ .

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

Move a negative from the denominator of $\frac{2}{- (x^{2} - 2)}$ to the numerator.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 2$ .

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

Rewrite $x^{4} - 4$ in a factored form.

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Rewrite $4$ as $2^{2}$ .

$\frac{{(x^{2})}^{2} - 2^{2}}{x^{2} - 2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 2$ .

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

Cancel the common factor of $x^{2} - 2$ .

Cancel the common factor.

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

Divide $x^{2} + 2$ by $1$ .

$x^{2} + 2$

Simplify (x^4-2)/(x^2-2)+2/(-x^2+2)

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