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
Step 1: Factor the denominator of the first term using the difference of squares formula, a^2 - b^2 = (a-b)(a+b). x^2 - y^2 = (x-y)(x+y) Step 2: Rewrite the denominator of the second term to match a factor in the first term's denominator. y - x = -(x - y) Step 3: Substitute these factored forms back into the original expression. (3x)/((x-y)(x+y)) - (x)/(-(x-y)) Step 4: Simplify the sign in the second term. (3x)/((x-y)(x+y)) + (x)/(x-y) Step 5: Find a common denominator, which is (x-y)(x+y). Multiply the second term by (x+y)/(x+y). (3x)/((x-y)(x+y)) + (x(x+y))/((x-y)(x+y)) Step 6: Combine the numerators over the common denominator. (3x + x(x+y))/((x-y)(x+y)) Step 7: Distribute x in the numerator and simplify. (3x + x^2 + xy)/((x-y)(x+y)) Step 8: Factor out x from the numerator. (x(3 + x + y))/((x-y)(x+y)) The simplified expression is: (x(x+y+3))/((x-y)(x+y)) Send me the next one 📸