A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)
A
\(\frac{-8}{15}\)
B
\(\frac{8}{15}\)
C
\(\frac{17}{15}\)
D
\(\frac{-17}{15}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(x \ast y = \frac{x^2 - y^2}{2xy}\)
=\(\frac{(x+y)(x-y)}{2xy}\)
-5 \(\ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\)
=\(\frac{-2 \times -8}{2(-5\times3)}\)
=\(\frac{-8}{15}\)
Source: Myschool Past Questions Archive (Record #9036)