This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems you sent: Problem 1: We need to simplify the expression (1)/(x-y) - (1)/(x+y) + (2x)/(x^2-y^2). We assume the third term's denominator is x^2-y^2, as this allows for simplification with the other terms. Step 1: Combine the first two fractions by finding a common denominator, which is (x-y)(x+y) = x^2-y^2. (1)/(x-y) - (1)/(x+y) = (1 · (x+y))/((x-y)(x+y)) - (1 · (x-y))/((x+y)(x-y)) = (x+y - (x-y))/(x^2-y^2) = (x+y-x+y)/(x^2-y^2) = (2y)/(x^2-y^2) Step 2: Add the result from Step 1 to the third fraction. (2y)/(x^2-y^2) + (2x)/(x^2-y^2) = (2y+2x)/(x^2-y^2) Step 3: Factor