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 numerator. The numerator is 15x^2 - 15y^2. We can factor out the common term 15. 15x^2 - 15y^2 = 15(x^2 - y^2) Recognize that x^2 - y^2 is a difference of squares, which factors as (x-y)(x+y). So, the numerator becomes: 15(x-y)(x+y) Step 2: Factor the denominator. The denominator is 5x^2 + 10xy + 5y^2. We can factor out the common term 5. 5x^2 + 10xy + 5y^2 = 5(x^2 + 2xy + y^2) Recognize that x^2 + 2xy + y^2 is a perfect square trinomial, which factors as (x+y)^2. So, the denominator becomes: 5(x+y)^2 Step 3: Rewrite the expression with the factored numerator and denominator. (15(x-y)(x+y))/(5(x+y)^2) Step 4: Simplify the expression by canceling common factors. Divide 15 by 5: (15)/(5) = 3. Cancel one (x+y) term from the numerator and the denominator: (x+y)/((x+y)^2) = (1)/(x+y). (3(x-y))/(x+y) The simplified expression is (3(x-y))/(x+y). That's 2 down. 3 left today — send the next one.