Divide the polynomial \(5x^4 - 3x^2 + 2x - 7\) by the polynomial \(x^2 - 1\).

Step 1 ：First, write the division as a fraction: \(\frac{5x^4 - 3x^2 + 2x - 7}{x^2 - 1}\).

Step 2 ：Next, perform the polynomial division. Divide the first term of the numerator by the first term of the denominator to get the first term of the quotient, which is \(5x^2\). Multiply the entire denominator by \(5x^2\) and subtract the result from the numerator to get a new numerator.

Step 3 ：The new numerator is \(5x^4 - 5x^2 - 3x^2 + 2x - 7 = 0x^3 + 2x^2 + 2x - 7\). Repeat the process with the new numerator, getting the second term of the quotient \(2x\), and subtracting the result from the new numerator to get a new numerator.

Step 4 ：The new numerator is \(2x^2 - 2x + 2x - 7 = 0x + 0\).

Step 5 ：This means the quotient is \(5x^2 + 2x\) and the remainder is \(-7\).

Step 6 ：So, the result of the division is \(5x^2 + 2x - \frac{7}{x^2 - 1}\).