(а⁴-1-а⁴-1+а²-1 ) /а²-1

To simplify the expression \((a^4 - 1 - a^4 - 1 + a^2 - 1) / (a^2 - 1)\), let's first simplify the numerator.

Starting with the numerator:

\[ a^4 - 1 - a^4 - 1 + a^2 - 1 \]

Combine like terms:

1. \(a^4 - a^4 = 0\)
2. \(-1 - 1 - 1 = -3\)

So, the numerator simplifies to:

\[ a^2 - 3 \]

Now, our expression becomes:

\[ \frac{a^2 - 3}{a^2 - 1} \]

The next step is to check if we can factor or further simplify the expression. The denominator \(a^2 - 1\) can be factored as \((a - 1)(a + 1)\), but the numerator \(a^2 - 3\) does not factor nicely over the reals.

Therefore, the simplified expression is:

\[ \frac{a^2 - 3}{a^2 - 1} \]

This is the most simplified form, unless further context or restrictions for \(a\) are provided.