Simplify the expression (1)/(((t2-1)-1)) + (2)/(((t2-1)+1))

The expression is:

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

Simplify the first denominator:

$$(t^2-1)-1 = t^2-2$$

Simplify the second denominator:

$$(t^2-1)+1 = t^2$$

The common denominator is $t^2(t^2-2)$.
Multiply the first term by $\frac{t^2}{t^2}$ and the second term by $\frac{t^2-2}{t^2-2}$:

$$\frac{1}{t^2-2} \cdot \frac{t^2}{t^2} + \frac{2}{t^2} \cdot \frac{t^2-2}{t^2-2}$$ $$= \frac{t^2}{t^2(t^2-2)} + \frac{2(t^2-2)}{t^2(t^2-2)}$$

$$= \frac{t^2 + 2(t^2-2)}{t^2(t^2-2)}$$ $$= \frac{t^2 + 2t^2 - 4}{t^2(t^2-2)}$$ $$= \frac{3t^2 - 4}{t^2(t^2-2)}$$

The simplified expression is $\frac{3t^2 - 4}{t^2(t^2-2)}$.