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
It looks like you're working on simplifying algebraic fractions. Based on the handwritten work below the initial expression, I will assume the problem is to add the two fractions, not multiply them. Step 1: Identify the expression to be simplified. The problem is to simplify the sum of the two algebraic fractions: (3)/(x-y) + (1)/(x+y) Step 2: Find a common denominator for the fractions. The denominators are (x-y) and (x+y). The least common denominator (LCD) is the product of these two distinct factors: (x-y)(x+y). Step 3: Rewrite each fraction with the common denominator. To rewrite the first fraction, multiply its numerator and denominator by (x+y): (3)/(x-y) = (3(x+y))/((x-y)(x+y)) To rewrite the second fraction, multiply its numerator and denominator by (x-y): (1)/(x+y) = (1(x-y))/((x+y)(x-y)) Step 4: Add the numerators over the common denominator. (3(x+y))/((x-y)(x+y)) + (1(x-y))/((x-y)(x+y)) = (3(x+y) + 1(x-y))/((x-y)(x+y)) Step 5: Expand and simplify the numerator. 3(x+y) + 1(x-y) = 3x + 3y + x - y Combine the like terms: (3x + x) + (3y - y) = 4x + 2y Step 6: Simplify the denominator. The denominator is (x-y)(x+y), which is a difference of squares: (x-y)(x+y) = x^2 - y^2 Step 7: Write the final simplified expression. Combine the simplified numerator and denominator: (4x+2y)/(x^2-y^2) The numerator can also be factored as 2(2x+y). (2(2x+y))/(x^2-y^2) Last free one today — make it count tomorrow, or type /upgrade for unlimited.