This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Step 1: State the given function. The function to be expressed in partial fractions is: f(x) = (2)/((x-1)(x+1)) Step 2: Set up the partial fraction decomposition. We assume the form: (2)/((x-1)(x+1)) = (A)/(x-1) + (B)/(x+1) To find A and B, multiply both sides by (x-1)(x+1): 2 = A(x+1) + B(x-1) Step 3: Solve for the constants A and B. To find A, set x=1: 2 = A(1+1) + B(1-1) 2 = 2A + 0 2 = 2A A = 1 To find B, set x=-1: 2 = A(-1+1) + B(-1-1) 2 = 0 + B(-2) 2 = -2B B = -1 Step 4: Write the final partial fraction expression. Substitute the values of A and B back into the decomposition: f(x) = (1)/(x-1) + (-1)/(x+1) f(x) = (1)/(x-1) - (1)/(x+1) The partial fraction decomposition of f(x) is (1)/(x-1) - (1)/(x+1). What's next?