Mathematics

A binary operation * on the set of rational numbers is defined as (x ast y…

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})
Correct Answer: Option 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(-5times3)}\
=frac{-2 times -8}{2(-5times3)}\
=frac{-8}{15})