A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 – y^2}{2xy}\). Find \(-5 \ast 3\)
-
\(\frac{-8}{15}\)
- \(\frac{8}{15}\)
- \(\frac{17}{15}\)
- \(\frac{-17}{15}\)
The correct answer is: A
Explanation
\(x \ast y = \frac{x^2 - y^2}{2xy}\\
=\frac{(x+y)(x-y)}{2xy}\\
-5 \ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\\
=\frac{-2 \times -8}{2(-5\times3)}\\
=\frac{-8}{15}\)