c. \( \frac{1}{x+1}+\frac{1}{x-1} \)

Let’s first combine the two fractions. The common denominator of \( (x+1)(x-1) \) allows us to rewrite the expression: \[ \frac{1}{x+1} + \frac{1}{x-1} = \frac{(x-1) + (x+1)}{(x+1)(x-1)} = \frac{2x}{(x+1)(x-1)} \] Now, upon simplifying, we can express it as: \[ \frac{2x}{x^2 - 1} \] This gives us a clearer view of the fraction's behavior, especially helpful in identifying vertical asymptotes and behaviors around key values such as \( x = 1 \) and \( x = -1 \). For practical applications, this type of expression is frequently encountered in calculus when dealing with limits and integrals. Understanding its form can help in finding areas under curves and solving real-world problems related to rates, such as fluid dynamics or population models where certain variables have to be constrained, showcasing the beauty of mathematical intersections with the natural world!