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
let's simplify this algebraic expression. Step 1: Rewrite the division as multiplication by the reciprocal of the second fraction. (x^2 - y^2)/(x^2 + xy) ÷ (2y - 2x)/(xy) = (x^2 - y^2)/(x^2 + xy) × (xy)/(2y - 2x) Step 2: Factorize the numerators and denominators. The numerator x^2 - y^2 is a difference of squares, which factors to (x-y)(x+y). The denominator x^2 + xy has a common factor of x, which factors to x(x+y). The numerator 2y - 2x has a common factor of 2, which factors to 2(y-x). We can also write y-x as -(x-y). The denominator xy is already in its simplest form. Substitute the factored forms into the expression: ((x-y)(x+y))/(x(x+y)) × (xy)/(2(-(x-y))) ((x-y)(x+y))/(x(x+y)) × (xy)/(-2(x-y)) Step 3: Cancel out common factors from the numerator and denominator. We can cancel (x+y) from the first fraction's numerator and denominator. We can cancel x from the denominator of the first fraction and the numerator of the second fraction. We can cancel (x-y) from the numerator of the first fraction and the denominator of the second fraction. (x-y)(x+y)x(x+y) × xy-2(x-y) Step 4: Write the simplified expression. 1 × (y)/(-2) = -(y)/(2) The simplified expression is: -(y)/(2) Drop the next question 📸