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's the solution to the problem. ((x+3x)^2)/(x^2-y^2) × (x-y)/(x+3x) Step 1: Simplify the terms inside the parentheses. (x+3x)^2 = (4x)^2 = 16x^2 x+3x = 4x Step 2: Substitute the simplified terms back into the expression. (16x^2)/(x^2-y^2) × (x-y)/(4x) Step 3: Factor the denominator x^2-y^2 using the difference of squares formula, a^2-b^2 = (a-b)(a+b). x^2-y^2 = (x-y)(x+y) Step 4: Substitute the factored denominator into the expression. (16x^2)/((x-y)(x+y)) × (x-y)/(4x) Step 5: Multiply the fractions and cancel out common factors (x-y) and 4x. (16x^2 (x-y))/((x-y)(x+y) (4x)) = (16x^2)/(4x(x+y)) Step 6: Simplify the remaining terms. (16x^2)/(4x(x+y)) = (4x)/(x+y) The simplified expression is (4x)/(x+y). What's next?