Find the derivative of (x^2 + 1) / (x^2 -1) using the quotient rule.

Here it is specified that the quotient rule has to be
used.

Now for finding the derivative of f(x)/g(x) the
quotient rule is [f’(x) g(x) – f(x) g’(x)]/ [g(x)] ^2

Here
f(x) = x^2+1. So we have f’(x) 2x.

g(x) = x^2 -1, so g’(x)
= 2x

Therefore the derivative of (x^2 + 1) / (x^2 -1)
is

[(x^2 - 1) * 2x – 2x * (x^2 +1)] / (x^2 -1)
^2

=> 2x [x^2 -1 – x^2 - 1] / (x^2 -1)
^2

=> -4x / (x^2 -1)
^2

=> -4x/(x^2 -1)
^2

Therefore the required result is - 4x/(x^2
-1) ^2