To divide the expression \(x^3+ 7x^2 - x - 7\) by \(x^2 - 1\), we can use polynomial long division. The process is similar to long division with numbers.

We start by dividing the first term of the dividend, \(x^3\), by the first term of the divisor, \(x^2\), to get \(x\).

We then multiply the divisor, \(x^2 - 1\), by this quotient, \(x\), to get \(x^3 - x\). We subtract this from the dividend to get a new polynomial, \(7x^2 - 7\).

We then repeat this process with the new polynomial.

The next step is to divide the first term of the new polynomial, \(7x^2\), by the first term of the divisor, \(x^2\), to get \(7\).

We then multiply the divisor, \(x^2 - 1\), by this quotient, \(7\), to get \(7x^2 - 7\). We subtract this from the new polynomial to get a remainder of 0.

So, the result of dividing \(x^3+ 7x^2 - x - 7\) by \(x^2 - 1\) is \(x + 7\) with a remainder of 0.