(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.