Final answer:
To find the partial fraction decomposition, express the rational function as a sum of simpler fractions and solve for the constants.
Step-by-step explanation:
To find the partial fraction decomposition of the rational function 2x/(x-1)(x+1), we need to express the rational function as a sum of simpler fractions. We can start by writing it as A/(x-1) + B/(x+1), where A and B are constants to be determined.
To find the values of A and B, we can create a common denominator for the two fractions and equate the numerators, which gives us 2x = A(x+1) + B(x-1). We can then solve for A and B by expanding and simplifying the equation.
Finally, we replace A and B in the partial fraction decomposition to get the final result.