The problem asks to find the expression for $\frac{f(x+h) - f(x)}{h}$ given that $f(x) = x^2 - 1$.

1. Problem Description

The problem asks to find the expression for $\frac{f(x+h) - f(x)}{h}$ given that $f(x) = x^2 - 1$.

2. Solution Steps

First, find the expression for $f(x+h)$.

$f(x+h) = (x+h)^2 - 1 = x^2 + 2xh + h^2 - 1$.

Next, calculate $f(x+h) - f(x)$.

$f(x+h) - f(x) = (x^2 + 2xh + h^2 - 1) - (x^2 - 1) = x^2 + 2xh + h^2 - 1 - x^2 + 1 = 2xh + h^2$.

Now, divide the result by $h$.

$\frac{f(x+h) - f(x)}{h} = \frac{2xh + h^2}{h} = \frac{h(2x + h)}{h} = 2x + h$.

3. Final Answer

The final answer is $2x + h$. The correct option is (c).