a binary operation ⊕ ⊕ o the set of rational numbers is defined as x ⊕ ⊕ y = x2−y22xy x 2 − y 2 2 x y . Find -5 ⊕ ⊕ 3

a binary operation $\oplus$ o the set of rational numbers is defined as x $\oplus$ y = $\frac{x^2-y^2}{2xy}$. Find -5 $\oplus$ 3

Answer Details

To find -5 ⊕ 3, we simply substitute x = -5 and y = 3 into the formula: -5 ⊕ 3 = (-5)^2 - 3^2 / (2 * -5 * 3) = 25 - 9 / (-30) = 16 / 30 = 8 / 15 Therefore, the answer is option D: 8-15. To explain how we arrived at this answer, we first plugged in the values of x and y into the formula for the binary operation ⊕. We then simplified the expression using basic arithmetic operations, following the order of operations (parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right). Finally, we expressed the result as a fraction in lowest terms.